Search

Pretopology and multisets have an essential role in mathematics, especially, in some real-life applications. This paper aims to establish a recombination between multisets and pretopology. In addition, some new types of multi-pretopological structures are constructed and some of their properties are investigated. Multi-pre-open sets and multi-pre-closure operator are investigated. Moreover, for the isotonic multi-pretopological structures, and the multi-pre-minimal closed subsets are introduced and studied. Also, the concept of m-pre-connected structures are established as an application of given results and some types of strongly connected structures are investigated. Finally, the effect of multisets in medical information systems has been studied. [ABSTRACT FROM AUTHOR]

In a space X, if for every countable open cover U = { U n : n ∈ N } of X, we can find a subcover V = { U m k : k ∈ N } such that δ ({ m k : U m k ∈ V }) = 0 then the space is called a statistically compact space. Extending the recent works of Sarkar, Bal, and Rakshit on statistically compactness, we investigate statistically compactness of a topological space in the star-operator’s background. The concept of star statistically compactness is contrasted to other topological features. This study explains the attributes of star statistically compactness and its subspaces under diverse circumstances, especially under open continuous surjection. [ABSTRACT FROM AUTHOR]

Let I C L (n) be the number of clopen topologies on a finite set of n elements. It is proved that the explicit formula for finding the total number of clopen topologies is ∑ k = 1 n S n , k = ∑ i = 1 n CL (n , 2 i) , where S n , k is the Stirling number of the second kind and CL (n , 2 i) is the number of clopen topologies having 2 i open sets, i = 1 , 2 , 3 ,... , n . Some results concerning the number of clopen topological spaces whose topologies have the same cardinality are also obtained. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new category of similarity measures, we begin to introduce the concept of effect matrix T ∧ (R 1 × R 2 × R 3 , p m , q n , f v) of type 3-tuple and study some of their properties. Moreover, from the soft set we find the pictures of type regular and irregular using effect matrix T ∧ (R 1 × R 2 × R 3 , p m , q n , f v) of type 3-tuple are found. An effect matrix T ∧ (R 1 × R 2 × R 3 , p m , q n , f v) of type 3-tuple is better than effect matrix T ∧ (ℜ 1 × ℜ 2 , p n , q m) of type 2-tuple, because we can deal with three different sets R 1 (a family of objectives), R 2 (a family of parameters), R 3 (a family of second parameters) in the same problem. This burden can be alleviated by application of type 3-tuple. Some applications of soft effect matrix of type 3-tuple T ∧ (R 1 × R 2 × R 3 , p m , q n , f v) in decision making problems are studied and explained. In this work we deal with pictures. Moreover, the similarity measure between two different soft sets under the same universal soft set (R 1 × R 2 × R 3) can be studied and explained its applications in medical diagnosis problems. [ABSTRACT FROM AUTHOR]

This paper constructs the compactification of rough pseudo metric spaces using the concept of Čech rough proximity spaces, in terms of rough linked grills which are generalizations of Cauchy sequences. [ABSTRACT FROM AUTHOR]

In this paper, we present a general framework for the study of rough sets using topological approaches. First, we introduce several concepts and properties of τ - R -open sets. After that, we used topology to generalize the basic rough set concepts and study their properties. It's application in data reduction and decision analysis is investigated. Finally, a simple example is adopted to demonstrate the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

In this paper, the authors continue studying more properties of somewhere dense sets. They derive some interesting results related to them such as the collection of all somewhere dense subsets of a strongly hyperconnected space (X , τ) forms a filter on X, and a topological space which contains at least two disjoint somewhere dense sets is an S T 1 -space. Then they introduce and study a concept of S-limit points of a soft set. Depending on somewhere dense and cs-dense sets, they also define and investigate various maps between topological spaces, namely SD-continuous, SD-irresolute, SD-open, SD-closed and SD-homeomorphism maps. [ABSTRACT FROM AUTHOR]

The notions of a s-T1 space, an almost generalized Hausdorff space, and a μ-locally compact space in the context of generalized topological spaces are introduced. Properties in relation to these spaces are established. Finally, a version of one point compactification of a s-T1 space is obtained. [ABSTRACT FROM AUTHOR]

We see that the real numbers system with the usual topology contains no minimal open sets. This observation instigates us to study topological spaces having no minimal and maximal open sets. We find that such topological spaces if connected are not cut-point spaces. We also characterize mean open sets in T1 connected topological spaces. [ABSTRACT FROM AUTHOR]

The aim of the present article is to introduce a kind of proximity structure, termed μ-proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of μ-proximity is given and it is shown that any generalized topology of a generalized topological space (X,μ) is always induced by a suitable μ-proximity if and only if (X,μ) satisfies a type of complete regularity condition. The notion of quasi μ-proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi μ-proximity, is proved. [ABSTRACT FROM AUTHOR]

In the note we discuss partial metric type structures and present their basic properties as well as their relationship with metric type structures. As an application, fixed point theorems for a Lipschitzian map on this structures will be presented. [ABSTRACT FROM AUTHOR]

In this work, we extend the Ilić and Rakočević's (Appl Math Lett 22(5):728-731, ) fixed point theorem for quasi-contraction mapping in cone metric spaces to the partial cone metric spaces. Among other things, we generalize recent results of Sönmez (Fixed point theorems in partial cone metric spaces, , ), Dey and Saha (TWMS J Appl Eng Math 3(1):1-9, ) and Malhotra et al. (Int J Math Arch 4(2):610-616, ). [ABSTRACT FROM AUTHOR]