Search

We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG : X → X / ∼G of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.

In this paper, we solve two problems concerning the ideally conjunctive join-semilattices. First, we show that L / R 1 (Id L) | L is ideally conjunctive for all join-semilattices L. Then we characterize those ideally conjunctive join-semilattices L such that coz a is compact for all a ∈ L. Moreover, we give the definition of conjunctive posets and prove that the category of ideally conjunctive join-semilattices and join homomorphisms is reflective in the category of conjunctive posets and weakly ideal-continuous maps. As a corollary, we obtain the free ideally conjunctive join-semilattices over conjunctive posets. [ABSTRACT FROM AUTHOR]

We show that for a nice partial action n with closed domain of a compact group G on a profinite space X the orbit space X/ ~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG: X → ~G of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of separately continuous actions on profinite spaces is reflective in the category of separately continuous actions on compact Hausdorff spaces. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce the notion of weak r-level LM-G-filter spaces and strong p-level LM-G-filter spaces and discuss certain properties of these spaces. The study identifies [Formula: see text]-G, the category of weak r-level LM-G-filter spaces as an isomorphism-closed bireflective full subcategory of LM-G, the category of LM-G-filter spaces. It is also proved that [Formula: see text]-G, the category of strong p-level LM-G-filter spaces is an isomorphism-closed bicoreflective full subcategory of LM-G. Moreover, level decompositions of LM-G-filter spaces are studied and some properties of the associated L-pre G-filter spaces are obtained.

This paper is devoted to the study of the T0 separation axiom for a neutrosophic topological space. We give a categorical study of these spaces in a special case of neutrosophic topological spaces called neutrosophic saturated topological spaces. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce catalyzed LM-G-filter spaces, a special case of weakly inspired LM-G-filter spaces and identify certain properties of these spaces. It is proved that CLM-G, the category of catalyzed LM-G-filter spaces, is isomorphic to ILM-G, the category of inspired LM-G-filter spaces. Moreover, the categorical connection between WILM-G, the category of weakly inspired LM-G-filter spaces, and CLM-G is investigated through interior and exterior catalyzation of weakly inspired LM-G-filter spaces. It is proved that CLM-G is an isomorphism-closed, bireflective and bicoreflective full subcategory of WILM-G and LM-G. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce the notion of weak r-level LM-G-filter spaces and strong p-level LM-G-filter spaces and discuss certain properties of these spaces. The study identifies W L M r -G, the category of weak r-level LM-G-filter spaces as an isomorphism-closed bireflective full subcategory of LM-G, the category of LM-G-filter spaces. It is also proved that S L M p -G, the category of strong p-level LM-G-filter spaces is an isomorphism-closed bicoreflective full subcategory of LM-G. Moreover, level decompositions of LM-G-filter spaces are studied and some properties of the associated L-pre G-filter spaces are obtained. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to solve two open problems in topological residuated lattices. In this paper, given a linear topological residuated lattice, we find sufficient and necessary conditions under which the original topology coincides with the new one induced by a system of filters of the residuated lattice. This result will be valid for finite and infinite BL -algebras, which is a complete answer to the open problem proposed by Zahiri and Borzooei in 2016 and improves the incomplete answer given by Yang et al. in 2018. Moreover, using the topology induced by a system of filters of a residuated lattice, we prove that the set of all filters of the residuated lattice and the set of all corresponding zero-dimensional linear topological residuated lattices have the same cardinality. This result gives a negative answer to the open problem proposed by Yang and Zhang in 2019. Finally, we show that the category of residuated lattices is the reflective subcategory of the category of linear topological residuated lattices. [ABSTRACT FROM AUTHOR]

Fuzzy closure operators play a significant role in fuzzy order theory. This paper aims to further enrich and improve the study of fuzzy closure operators. Based on the work of Bělohlávek and Yao, we shall continue to study the relative properties of fuzzy closure operators. First, we shall consider the extensions of L-subsets via fuzzy closure operators. Then we give an application of fuzzy closure operators, that is, by fuzzy closure operators we shall prove that the category CFPos of complete fuzzy posets and their fuzzy-join preserving maps is a reflective full subcategory of FPost, where FPost denotes the category of fuzzy posets and their fuzzy-existing-join preserving maps. [ABSTRACT FROM AUTHOR]

Motivated by certain types of ideals in pointfree functions rings, we define what we call P-sublocales in completely regular frames. They are the closed sublocales that are interior to the zero-sublocales containing them. We call an element of a frame L that induces a P-sublocale a P-element, and denote by Pel (L) the set of all such elements. We show that if L is basically disconnected, then Pel (L) is a frame and, in fact, a dense sublocale of L. Ordered by inclusion, the set S p (L) of P-sublocales of L is a complete lattice, and, for basically disconnected L, S p (L) is a frame if and only if Pel (L) is the smallest dense sublocale of L. Furthermore, for basically disconnected L, S p (L) is a sublocale of the frame S c (L) consisting of joins of closed sublocales of L if and only if L is Boolean. For extremally disconnected L, iterating through the ordinals (taking intersections at limit ordinals) yields an ordinal sequence L ⊇ Pel (L) ⊇ Pel 2 (L) ⊇ ⋯ ⊇ Pel α (L) ⊇ Pel α + 1 (L) ⊇ ⋯ that stabilizes at an extremally disconnected P-frame, that we denote by Pel ∞ (L) . It turns out that Pel ∞ (L) is the reflection to L from extremally disconnected P-frames when morphisms are suitably restricted. [ABSTRACT FROM AUTHOR]

We show that for a field K and n ≥ 1 {n\geq 1} , the soberification 𝒮 ⁢ (𝔸 n ⁢ (K)) {\mathcal{S}(\mathbb{A}^{n}(K))} of the affine n-space 𝔸 n ⁢ (K) {\mathbb{A}^{n}(K)} over K is homeomorphic to its spectralization ℬ ⁢ 𝒮 ⁢ (𝔸 n ⁢ (K)) {\mathcal{BS}(\mathbb{A}^{n}(K))} , and it can be embedded into the spectrum Spec ⁢ (K ⁢ [ X 1 , ... , X n ]) {\mathrm{Spec}(K[X_{1},\dots,X_{n}])}. Moreover, if the field K is algebraically closed, then there are homeomorphisms 𝒮 ⁢ (𝔸 n ⁢ (K)) ≈ ℬ ⁢ 𝒮 ⁢ (𝔸 n ⁢ (K)) ≈ Spec ⁢ (K ⁢ [ X 1 , ... , X n ]) \mathcal{S}(\mathbb{A}^{n}(K))\approx\mathcal{BS}(\mathbb{A}^{n}(K))\approx% \mathrm{Spec}(K[X_{1},\dots,X_{n}]). We also show that for a space X, the subspace z ⁢ Spec ⁢ (C ⁢ (X)) ⊆ Spec ⁢ (C ⁢ (X)) z\mathrm{Spec}(C(X))\subseteq\mathrm{Spec}(C(X)) of prime z-ideals of the ring C ⁢ (X) {C(X)} of real-valued continuous functions on X is homeomorphic to the space z ⁢ 𝒮 ⁢ ℛ ⁢ (X) {z\mathcal{SR}(X)} of prime z-filters with an appropriate topology and there is a homeomorphism ℬ ⁢ 𝒮 ⁢ (X) ≈ z ⁢ Spec ⁢ (C ⁢ (X)) {\mathcal{BS}(X)\approx z\mathrm{Spec}(C(X))} provided X is perfectly normal. [ABSTRACT FROM AUTHOR]

In this paper, a new approach to fuzzy convergence theory in the framework of stratified L-topological spaces is provided. Firstly, the concept of stratified L-prefilter convergence structures is introduced and it is shown that the resulting category is a Cartesian closed topological category. Secondly, the relations between the category of stratified L-prefilter convergence spaces and the category of stratified L-topological spaces are studied and it is proved that the latter can be embedded in the former as a reflective subcategory. Finally, the relations between the category of stratified L-prefilter convergence spaces and the category of stratified L-Min convergence spaces (fuzzy convergence spaces in the sense of Min) are investigated and it is shown that the former can be embedded in the latter as a reflective subcategory. [ABSTRACT FROM AUTHOR]

We study the uniform connection properties of uniform local connectedness, a weaker variant of the latter, and a certain property S in the context of nearness frames. We show that the uniformly locally connected nearness frames form a reflective subcategory of the category of nearness frames whose underlying frame is locally connected. Amongst other results we show that these uniform connection properties are conserved and reflected by perfect nearness extensions which are uniformly regular. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the concept of extensional L-fuzzy Q-convergence structures is proposed. It is shown that there is an adjunction between the category of extensional L-fuzzy topological spaces and the category of extensional L-fuzzy topological spaces. In particular, the category of extensional L-fuzzy topological spaces can be embedded in the category of extensional L-fuzzy Q-convergence spaces as a reflective subcategory. Also, the notion of topological extensional L-fuzzy Q-convergence spaces is introduced and the resulting category is shown to be isomorphic to the category of extensional L-fuzzy topological spaces. [ABSTRACT FROM AUTHOR]

Following the concept of topological theory of S.E. Rodabaugh, this paper introduces a new approach to (lattice-valued) bornology, which is based in bornological theories, and which is called variety-based bornology. In particular, motivated by the notion of topological system of S. Vickers, we introduce the concept of variety-based bornological system, and show that the category of variety-based bornological spaces is isomorphic to a full reflective subcategory of the category of variety-based bornological systems. [ABSTRACT FROM AUTHOR]

In this paper, based on a complete residuated lattice, we introduce the concept of fuzzy cut-stable maps and discuss the relationship between fuzzy cut-stable maps and some special maps. We also obtain the extension property of fuzzy cut-stable maps. Furthermore, it is proved that the category of fuzzy complete (continuous) lattices with fuzzy complete homomorphisms is a full reflective subcategory of the category of fuzzy (precontinuous) posets with fuzzy cut-stable maps. [ABSTRACT FROM AUTHOR]

Are all subcategories of locally finitely presentable categories that are closed under limits and ƛ-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case ƛ = ... the answer is affirmative also for all iso-full subcategories, i. e., those containing with every pair of objects all isomorphisms between them. We discuss a possible generalization of this from ... to an arbitrary ƛ. [ABSTRACT FROM AUTHOR]

This paper extends the Day Reflection Theorem to skew monoidal categories. We also provide conditions under which a skew monoidal structure can be lifted to the category of Eilenberg-Moore algebras for a comonad. [ABSTRACT FROM AUTHOR]

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the L'evy hierarchy. For example, the statement that, for a class S of morphisms in a locally presentable category C of structures, the orthogonal class of objects is a small-orthogonality class (hence reflective) can be proved in ZFC if S is 61, while it follows from the existence of a proper class of supercompact cardinals if S is 62, and from the existence of a proper class of what we call C.n/-extendible cardinals if S is 6nC2 for n = 1. These cardinals form a new hierarchy, and we show that Vopenka's principle is equivalent to the existence of C.n/-extendible cardinals for all n. As a consequence of our approach, we prove that the existence of cohomological localizations of simplicial sets, a long-standing open problem in algebraic topology, is implied by the existence of arbitrarily large supercompact cardinals. This follows from the fact that E'-equivalence classes are 62, where E denotes a spectrum treated as a parameter. In contrast with this fact, E'-equivalence classes are 61, from which it follows (as is well known) that the existence of homological localizations is provable in ZFC. [ABSTRACT FROM AUTHOR]