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In this study, we generalized two known open sets called semi-open and h-open sets to find a new type called semi-h-open set in topological space We have presented the relationship of several famous open sets to this set. We have also studied the semi-h-open continuity in topological space. In this study, we generalized two known open sets called semi-open and h-open sets to find a new type called semi-h-open set in topological space We have presented the relationship of several famous open sets to this set. We have also studied the semi-h-open continuity in topological space. we generalized two known open sets.

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine's notions of generalized closed sets and Maki's  Λ  sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine's generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine's method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of  Λ -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. [ABSTRACT FROM AUTHOR]

The paper initially investigates semi-topological properties of the Khalimsky (K-, for brevity) topological version of the classical Jordan curve theorem. Assume a simple closed K-curve with l elements in (Z 2 , κ 2) that is the K-topological plane, denoted by C K l for brevity. Then every C K l separates ( Z 2 , κ 2) into exactly two nonempty components that may be neither open nor closed in ( Z 2 , κ 2) . Hence we need to investigate semi-topological features of C K l and Z 2 \ C K l in (Z 2 , κ 2) . We first show that not every C K l is always semi-open or semi-closed in (Z 2 , κ 2) . Second, we find a condition for C K l to be either semi-open or semi-closed in (Z 2 , κ 2) . After establishing a continuous analog of C K l denoted by A (C K l) (⊂ R 2) , we show that A (C K l) is both semi-open and semi-closed in (R 2 , U) that is the 2-dimensional real plane with the usual topology. Besides, we show that A (C K l) always separates (R 2 , U) into two non-empty components, denoted by C and D, that are both semi-open and semi-closed to obtain a partition of R 2 , i.e., { C , D , A (C K l) } . Finally, we obtain a partition of Z 2 , i.e., { I (C K l) , O (C K l) , C K l } and prove that each of I (C K l) and O (C K l) is semi-closed and it need not be semi-open, where I (C K l) and O (C K l) are called an inside and outside of C K l , respectively. [ABSTRACT FROM AUTHOR]

Patch tests are the gold standard in the work-up of allergic contact dermatitis. Apart from commercial products, it is also of utmost importance to include the patients' own products. Products with unknown content or containing strong irritant, corrosive, toxic or poisonous chemicals should never be patch-tested, though. Recommendations on how to patch-test finished products can easily be retrieved in the literature and in specialised reference books; practical advice on test modalities (test methods, concentrations, vehicles) have been outlined for leave-on and rinse-off cosmetics, household detergents, chemical products (glues, paints), solid materials (gloves, shoes, textiles, leather goods, metal, plastic and rubber items), occupational products, plants, woods and food items. Separate guidelines exist on how to patch-test drugs. Whenever a positive or negative reaction to a product is obtained, practitioners should always question the possibility of a false-positive or a false-negative reaction, respectively. In these cases, additional test procedures may be required (eg testing of separate ingredients, repeated open-application tests, serial dilutions of a chemical or product, glove-repeated application tests). In this article we provide a practical overview for clinicians on how to test patients' own products. [ABSTRACT FROM AUTHOR]

The concept of relative topological properties was introduced by Arhangel'skii and Gennedi and was subsequently investigated by many authors for different notions of general topology. In this paper few semi-separation axioms in relative sense are introduced and studied by utilizing semi-open sets. Characterizations and preservation under mapping of these newly defined notions are provided. Relationship that exists between these notions, with some of the absolute properties and with the existing relative separation axioms are investigated. [ABSTRACT FROM AUTHOR]

The paper initially develops the semi-Jordan curve theorem on the digital plane with the Marcus-Wyse topology, i.e., $ MW $-topological plane or $ ({\mathbb Z}^2, \gamma) $ for brevity. We first prove that while every simple closed $ MW $-curve is semi-open in $ ({\mathbb Z}^2, \gamma) $, it may not be semi-closed. Given a simple closed $ MW $-curve with $ l $ elements, denoted by $ SC_{\gamma}^l $, after establishing a continuous analog of $ SC_{\gamma}^l $ denoted by $ \mathcal{A}(SC_{\gamma}^l) $, we initially show that $ \mathcal{A}(SC_{\gamma}^l) $ is both semi-open and semi-closed in $ ({\mathbb R}^2, \mathcal{U}) $, where $ ({\mathbb R}^2, \mathcal{U}) $ is the $ 2 $-dimensional real plane $ {\mathbb R}^2 $ with the usual topology $ \mathcal{U} $. Furthermore, we find a condition for $ \mathcal{A}(SC_{\gamma}^l) $ to separate $ ({\mathbb R}^2, \mathcal{U}) $ into exactly two non-empty components, compared to a typical Jordan curve theorem on $ ({\mathbb R}^2, \mathcal{U}) $. Since not every $ SC_{\gamma}^l $ always separates ($ {\mathbb Z}^2, \gamma) $ into two nonempty components, we find a condition for $ SC_{\gamma}^l, l\neq 4, $ to separate $ ({\mathbb Z}^2, \gamma) $ into exactly two components. The semi-Jordan curve theorem on the $ MW $-topological plane plays an important role in applied topology such as digital topology, mathematical morphology as well as computer science.

The paper initially develops the semi-Jordan curve theorem on the digital plane with the Marcus-Wyse topology, i.e., M W -topological plane or ( Z 2 , γ) for brevity. We first prove that while every simple closed M W -curve is semi-open in ( Z 2 , γ) , it may not be semi-closed. Given a simple closed M W -curve with l elements, denoted by S C γ l , after establishing a continuous analog of S C γ l denoted by A (S C γ l) , we initially show that A (S C γ l) is both semi-open and semi-closed in ( R 2 , U) , where ( R 2 , U) is the 2 -dimensional real plane R 2 with the usual topology U . Furthermore, we find a condition for A (S C γ l) to separate ( R 2 , U) into exactly two non-empty components, compared to a typical Jordan curve theorem on ( R 2 , U). Since not every S C γ l always separates ( Z 2 , γ) into two nonempty components, we find a condition for S C γ l , l ≠ 4 , to separate ( Z 2 , γ) into exactly two components. The semi-Jordan curve theorem on the M W -topological plane plays an important role in applied topology such as digital topology, mathematical morphology as well as computer science. [ABSTRACT FROM AUTHOR]

Since the Marcus-Wyse ($ MW $-, for brevity) topological spaces play important roles in the fields of pure and applied topology (see Remark 2.2), the paper initially proves that the $ MW $-topological space satisfies the semi-$ T_3 $-separation axiom. To do this work more efficiently, we first propose several techniques discriminating between the semi-openness or the semi-closedness of a set in the $ MW $-topological space. Using this approach, we suggest the condition for simple $ MW $-paths to be semi-closed, which confirms that while every $ MW $-path $ P $ with $ \vert\, P\, \vert\geq 2 $ is semi-open, it may not be semi-closed. Besides, for each point $ p \in {\mathbb Z}^2 $ the smallest open neighborhood of the point $ p $ is proved to be a regular open set so that it is semi-closed. Note that the $ MW $-topological space is proved to satisfy the semi-$ T_3 $-separation axiom, i.e., it is proved to be a semi-$ T_3 $-space so that we can confirm that it also satisfies an $ s $-$ T_3 $-separation axiom. Finally, we prove that the semi-$ T_3 $-separation axiom is a semi-topological property.

• The prototype varies within 15 % in ambient temperature range of −30 ∼ 7℃. • The frosting has no impact on the overall efficiency of system. • It has the potential for application in the field of high temperature heating. • Utilizing high-efficiency compressors could improve the system's coefficient of performance by 13.47 ∼ 31.50 %. Different from conventional vapor compression heat pump system, this investigation presented a semi-open air cycle heat pump system, whose performance was experimentally assessed across diverse conditions. The prototype showcased stable heating performance with coefficient of performance surpassing 1.0 at ambient temperatures above −7°C and maintaining its variation within 15 % in the ambient temperature range of (−30 ∼ 7) °C. According to the analysis of the experimental results, although frosting has an impact on some parameters, the overall efficiency of the system remains stable over time. These special designs of high-pressure ratio and oil cooling of compressor could make the system temperature reaching 132 °C, indicating that the system has the potential for application in the field of high temperature heating. Heat exchanger analysis revealed an imbalance in heat exchange ratios between oil–water heat exchanger and air–water heat exchanger. The prototype achieved 58 ∼ 72 % of a significant conversion efficiency of electric energy to oil internal energy, proposing that utilizing high compression efficiency compressors could enhance system coefficient of performance by (13.47 ∼ 31.50)%. The isentropic efficiency and expansion work recovery efficiency of booster turbo-expander were calculated as (59 ∼ 65)% and (33 ∼ 40)% respectively. Additionally, it was found that frosting could optimize the recovery rate of expansion work under specific conditions. [ABSTRACT FROM AUTHOR]

An S-Topological BE-Algebras(STBE-Algebras) is a BE-Algebra equipped with a special type of topology that makes the operation (defined on it)as S-topological continuous. In this paper, we discuss the separation axioms on a STBE-Algebras. [ABSTRACT FROM AUTHOR]

In this paper we introduce and study the notion of ωc-set. We also study ω-sets, as complements of ωc-sets. Finally, using the ωc-sets and ω-sets of a topological space, we introduce and study the notion of ω-extremally disconnected topological spaces. We obtain a result akin to Urysohn's Lemma in the setting of ω-extremally disconnected topological spaces. [ABSTRACT FROM AUTHOR]

The question as to the number of sets obtainable from a given subset of a topological space using the operators derived by composing members of the set {b, i, ∨, ∧}, where b, i, ∨ and ∧ denote the closure operator, the interior operator, the binary operators corresponding to union and intersection, respectively, is called the Kuratowski {b, i, ∨, ∧}-problem. This problem has been solved independently by Sherman [21] and, Gardner and Jackson [13], where the resulting 34 plus identity operators were depicted in the Hasse diagram. In this paper we investigate the sets of fixed points of these operators. We show that there are at most 23 such families of subsets. Twelve of them are the topology, the family of all closed subsets plus, well known generalizations of open sets, plus the families of their complements. Each of the other 11 families forms a complete complemented lattice under the operations of join, meet and negation defined according to a uniform procedure. Two of them are the well known Boolean algebras formed by the regular open sets and regular closed sets, any of the others in general need not be a Boolean algebras. [ABSTRACT FROM AUTHOR]

In this paper, we initiate the concept of semi open sets in ideal closure spaces. In particular, we deliberate the properties of semi- open and semi-closed sets, union and intersection of semi open subsets in ideal closure spaces. Along with we make some views on semi separation axioms in ideal closure spaces. [ABSTRACT FROM AUTHOR]

Highlights • Grazing has no effects on the communities of ectomycorrhizal fungi. • Historical land-use intensity has a negative effect on species richness. • Proportion of broadleaved trees, soil pH and moisture drives communities. • Stand conditions should be evaluated when planning wood-pasture conservation. Abstract Traditional rural biotopes such as wood-pastures are species-rich environments that have been created by low-intensity agriculture. Their amount has decreased dramatically during the 20th century in whole Europe due to the intensification of agriculture. Wood-pastures host some fungal species that prefer warm areas and are adapted to semi-open conditions, but still very little is known about fungi in these habitats. We studied how management, historical land-use intensity, present grazing intensity, time since abandonment, and stand conditions affect the species richness and community composition of ectomycorrhizal fungi. We surveyed fruit bodies on three 10 m × 10 m study plots in 36 sites and repeated the surveys three times. Half of the sites were currently unmanaged but had a grazing history. We measured soil pH, soil moisture and the basal area of different tree species, and interviewed landowners about grazing history. We found that the proportion of broadleaved trees, soil pH, and soil moisture are the major drivers of the communities of ectomycorrhizal fungi in boreal wood-pastures. Management or grazing intensity did not have significant effects on fungal species richness, whereas historical land-use intensity seemed to have a negative effect on species richness. To conclude, present stand conditions are the most important factors to evaluate when planning the conservation of ectomycorrhizal fungi living in semi-open forest habitats. [ABSTRACT FROM AUTHOR]

The classical version of Baire category theorem was proved independently in 1897 by W. Osgood [Non-uniform convergence and the integration of series term by term, Amer. J. Math., 19 (1897), 155-190] and in 1899 by R. Baire [Sur les fonctions de variable reeles, Annali di Mat. Pura et Appi., 3 (1899), 65]. Our paper offers several characterizations and properties of Baire spaces with respect to the class of semi-open sets. Generalizations of Baire Category Theorem in this context are established. [ABSTRACT FROM AUTHOR]

Sorption systems traditionally fall into two categories: closed (for chilling and heat pumping) and open (for dehumidification). Recent work has explored the possibility of semi-open systems, which can perform heat pumping or chilling while utilizing ambient humidity as the working fluid of the cycle, and are capable of being driven by solar, waste, or combustion heat sources. The efficiencies of closed and open systems are well characterized and can be accurately determined from four temperatures (one for each of the main components—desorber, absorber, condenser and evaporator). In this work, the performance potential of semi-open systems is explored by adapting expressions for the efficiency of closed and open systems to the novel semi-open systems. A key new parameter is introduced, which involves both the ambient dry bulb and ambient dew point temperature, since both are critical to semi-open absorber operation. The dew point temperature is necessary to capture the absorption performance, while the dry bulb temperature is needed to calculate sensible heat transfer with surrounding air. [ABSTRACT FROM AUTHOR]

Wood-pastures are threatened anthropogenic biotopes that provide habitat for an extensive group of species. Here we studied the effect of management, grazing intensity, time since abandonment, historical land-use intensity, soil properties and stand conditions on communities of saprotrophic fungi in wood-pastures in Central Finland. We found that the proportion of broadleaved trees and soil pH are the major drivers in the communities of saprotrophic fungi in these boreal wood-pastures. In addition, tree species richness, soil moisture, historical land-use intensity and time since abandonment affected the communities of saprotrophic fungi. Current management or grazing intensity did not have a clear effect on saprotrophic fungal species richness, although dung-inhabiting fungal species richness was highest at intermediate to high grazing intensity. Obviously, there were many more dung-inhabiting fungal species on grazed than on abandoned sites. Our study highlights the conservation value of wood-pastures as hotspots of saprotrophic fungi. • Management or grazing intensity did not have clear effect on species richness. • Trees and soil pH were the major drivers in the communities of saprotrophic fungi. • Species richness increased with tree species richness and time since abandonment. • Stand conditions affect communities of saprotrophic fungi more than grazing. • Stand conditions should be evaluated when planning conservation of wood-pastures. [ABSTRACT FROM AUTHOR]

In this paper, we study the notion of S-paracompact spaces in ideal topological spaces. We provide some characterizations of these spaces and investigate relationships to other classes of spaces. Moreover, we study the invariance of such spaces under some special types of functions. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of mappings, namely, strongly na-continuous mappings. This class lies properly between the class of super I-continuous mappings and the class of strongly continuous mappings due to Levine. Some characterizations and basic properties of these mappings are obtained. The relationships among these mappings and some other stronger forms of continuity are also investigated. [ABSTRACT FROM AUTHOR]

We define and study strong SH-open sets, SH-sets and Sβ-H-sets. [ABSTRACT FROM AUTHOR]

An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset (heredity) and finite unions (additivity). Given a topological space (X,τ) an ideal ℐ on X and A⊆X, ψ(A) is defined as ⋃{U∈τ:U−A∈ℐ}. A topology, denoted τ*, finer than τ is generated by the basis {U−I:U∈τ,I∈ℐ}, and a topology, denoted 〈ψ(τ)〉, coarser than τ is generated by the basis ψ(τ)={ψ(U):U∈τ}. The notation (X,τ,ϑ) denotes a topological space (X,τ) with an ideal ℐ on X. A bijection f:(X,τ,ℐ)→(Y,σ,J) is called a *-homeomorphism if f:(X,τ*)→(Y,σ*) is a homeomorphism, and is called a ψ-homeomorphism if f:(X,〈ψ(τ)〉)→(Y,〈ψ(σ)〉) is a homeomorphism. Properties preserved by *-homeomorphisms are studied as well as necessary and sufficient conditions for a ψ -homeomorphism to be a *-homeomorphism. The semi-homeomorphisms and semi-topological properties of Crossley and Hildebrand [Fund. Math., LXXIV (1972), 233-254] are shown to be special case.

Introduction: We describe a semi-open approach to percutaneous tracheostomy as an effective and potentially safer alternative to open tracheostomy or percutaneous techniques in burn patients. Methods: We identified patients who underwent the modified technique from 2005 to 2007. Our method used a 2–3cm incision and limited dissection to the pretracheal fascia. A needle was used to enter the trachea and insert a guidewire. The trachea was then dilated using a ‘Blue Rhino’ dilator. The remainder of the procedure was performed according to standard technique. Results: 39 patients were identified. 30 of these cases were performed at the bedside. The average time to tracheostomy was 19days. The average total body surface area involved was 42%. 51% of patients had burns of the neck. Five patients had burns over the stomal site. Of these five, three required autografting prior to tracheostomy. There were no deaths related to the procedure and the only complication was intraoperative hemorrhage in one patient, which was readily controlled. Conclusion: The semi-open modification of the percutaneous tracheostomy combines the convenience and minimally invasive advantages of the percutaneous technique with the better surgical control of the airway afforded by the traditional open technique. [Copyright &y& Elsevier]

The flow driving performance data of a dirty air fan with a semi-open centrifugal impeller and a squirrel volute, designed for household vacuum cleaners, are experimentally obtained with the industry standard tests. The fluid flows in the fan at various conditions are numerically simulated. The agreements between the numerical data and the experimental results are reasonably good. The model-simulated flow structures show that air flow passes over the blade between the impeller blade channels. A high-velocity spot is formed at the top of each blade. The leakage flow, from the fluid-collecting squirrel back to the blade channels, represents a waste of the fluid dynamic energy and the pressure potential energy. However, such leakage flow presses the inlet air to the bottom disc of the impeller and helps in preventing the solid objects from getting to the blade top. Flow energy analysis shows that the main energy loss is in the semi-open impeller. The leakage flow and the disagreements between the flow direction and the blade angles at the leading and the trailing tips are the main causes of the low energy efficiency of the fan. [ABSTRACT FROM AUTHOR]

The article offers information on a type of covering dimension, indicating its properties and characterizations. It cites the use of alpha-open sets in topological spaces to present a type of covering dimension. Moreover, it indicates that every finite alpha-open cover of X has an alpha-open refinement of order not exceeding n, thus the alpha-covering dimension of a topological space is the least positive integer.

Abstract: Two surveys of the thermal environment and thermal sensations were conducted in the indoor and the semi-open spaces of traditional houses, during both summer and winter, in five districts of Nepal: Banke, Bhaktapur, Dhading, Kaski and Solukhumbu. The surveys were carried out for 40 days, gathering a total of 7116 thermal sensations from 103 subjects. The results show that residents are highly satisfied with the thermal condition of their houses, since they adjust well to the thermal conditions. The residents have higher neutral temperatures in semi-open spaces such as verandas than in indoor spaces. The findings reveal that people in the regions studied adapt well to the natural environment, as a result of which neutral temperatures are different in different climates. They are lowest in the cool climate, medium in the temperate climate and highest in the sub-tropical climate. [ABSTRACT FROM AUTHOR]

The structure of the class of S-disconnected spaces is studied. Two types of S-disconnectedness of topological spaces are introduced. Properties of these spaces in the context of connectedness of spaces are investigated. [ABSTRACT FROM AUTHOR]

The definition of the product of topologies is generalized in such a way that topologies are replaced by generalized topologies in the sense of [3]. [ABSTRACT FROM AUTHOR]

Optimal mappings and optimally irresolute mappings are introduced. Fundamental properties of them are obtained. Preservation of well-known separation axioms (semi-ℐ2, ℐ2, semi-normality, normality, s-regularity, regularity) under such types of mappings (with some additional conditions) is studied. [ABSTRACT FROM AUTHOR]

A 2.5-Å resolution structure of calcium-free calmodulin (CaM) bound to the first two IQ motifs of the murine myosin V heavy chain reveals an unusual CaM conformation. The C-terminal lobe of each CaM adopts a semi-open conformation that grips the first part of the IQ motif (lQxxxR). whereas the N-terminal lobe adopts a closed conformation that interacts more weakly with the second part of the motif (GxxxR). Variable residues in the lQ motif play a critical role in determining the precise structure of the bound CaM, such that even the consensus residues of different motifs show unique interactions with CaM. This complex serves as a model for the lever arm region of many classes of unconventional myosins, as well as other IQ motif-containing proteins such as neuromodulin and IQGAPs. [ABSTRACT FROM AUTHOR]

Several concepts generalizing the notion of connectedness of a topological space are investigated. It is obtained that some of these concepts are equivalent (without or with additional conditions). [ABSTRACT FROM AUTHOR]

We introduce the class of S-paracompact spaces as a generalization of paracompact spaces. A space ( X,T) is S-paracompact if every open cover of X has a locally finite semi-open refinement. We characterize S-paracompact spaces and study their basic properties. The relationships between S-paracompact spaces and other well-known spaces are investigated. [ABSTRACT FROM AUTHOR]

In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened. [ABSTRACT FROM AUTHOR]

We introduce a new class of functions called strongly precontinuous functions in topological spaces. Some properties and several characterizations of this type of functions are obtained. We investigate the relationships between this class of functions and other classes of non-continuous functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to continue the study of sg-compact spaces. The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces. In our paper we shall consider sg-compactness in product spaces. Our main result says that if a product space is sg-compact, then either all factor spaces are finite, or exactly one factor space is infinite and sg-compact and the remaining ones are finite and locally indiscrete. [ABSTRACT FROM AUTHOR]

Some properties of two classes of functions (p.a.α.c. and p.s.w.c) are studied. [ABSTRACT FROM AUTHOR]

Joseph and Kwack [Proc. Amer. Math. Soc. 80 (1980) 341–348] introduced the notion of (θ,s)-continuous functions in order to investigate S-closed spaces due to Thompson [Proc. Amer. Math. Soc. 60 (1976) 335–338]. In this paper, further properties of (θ,s)-continuous functions are obtained and relationships between (θ,s)-continuity, contra-continuity and regular set-connectedness defined by Dontchev et al. [Internat. J. Math. Math. Sci. 19 (1996) 303–310 and elsewhere] are investigated. [Copyright &y& Elsevier]

Joseph and Kwack [9] introduced the notion of (θ, s)-continuous functions in order to investigate S-closed spaces due to Thompson [32]. In [26], the present authors investigated further properties of (θ, s)-continuous functions. In this paper, we introduce a new class of functions called α-quasi-irresolute functions which is weaker than (θ, s)-continuous and improve some results established in [26]. [ABSTRACT FROM AUTHOR]

Noiri et al. in [16] introduced and investigated the notion of almost s-continuous functions. The object of this paper is to investigate some more properties of this type of functions. [ABSTRACT FROM AUTHOR]

Closed patch testing and the nitrocellulose-replica method are performed as useful clinical methods for the evaluation of human skin irritation by cosmetics and topical medicaments. Comparison of the sensitivity between microscopic scoring by nitrocellulose-replica method and visual scoring by closed patch test in the detection of skin irritation, however, has not been well studied with statistical analysis. Here, we evaluated human skin irritation by carboxylic acids, alcohols, esters and aldehydes, with different chain length (C8-C18), using both methods. The results of closed patch testing showed that, although the score of skin irritation for carboxylic acids (C8, C12), alcohols (C8) and aldehydes (C8), tested at a concentration of 0.5 m-2.0 m, significantly increased with increasing concentration of the test compounds, ester compounds scarcely caused any irritation on the surface of the skin occluded. In addition, an increase of carbon chain length in the test compounds made it impossible to detect skin irritation. In contrast, the nitrocellulose-replica method could evaluate skin reactions against very weak irritants that gave no macroscopic alterations on the skin surface in the closed patch test. However, the scoring system is somewhat subjective and should be improved to make the analysis more objective. [ABSTRACT FROM AUTHOR]

We will show that a system is synchronized if and only if it has a cover whose cover map is semi-open. Also, any factor code on an irreducible sofic shift is semi-open and the image of a synchronized system by a semi-open code is synchronized. On the other side, right-closing semi-open extension of an irreducible shift of finite type is of finite type. Moreover, we give conditions on finite-to-one factor codes to be open and show that any semi-open code on a synchronized system is bi-continuing a.e. We give some sufficient conditions for a right-continuing a.e. factor code being right-continuing everywhere. [ABSTRACT FROM AUTHOR]

In a recent paper by T. Noiri [1], a function f:X→Y is said to be weakly α-continuous if f:Xα→Y is weakly continuous where Xα is the space X endowed with the α-topolooy. Smilarly, we define subweak α-continuity and almost α-continuity and show that almost α-continuity coincides with the almost continuity of T. Husain [2] and H. Blumberg [3]. This implies a functional tridecomposition of continuity using almost continuity and subweak α-continuity.