On elementary soft compact topological spaces

arXiv (Cornell University), 2018

The notion of soft topology was introduced very recently, built up on soft elementary intersection and union. In this paper, Based on this approach, we introduce the notion of soft elementary compact sets and spaces. Also, we investigate their properties. To that end we prove the soft elementary version of Baire theorem.

Benchalli et al. [4] introduced the notion of soft β-compactness by using soft filter basis. In continuation, in this paper we further study some more properties of soft β-compactness in soft topological spaces. Furthermore we introduce and discuss, soft β-first countable, soft β-second countable spaces, soft β-closed spaces and soft generalized β-compact spaces in soft topological spaces.

The main purpose of this paper is to introduce soft µ-compact soft generalized topological spaces as a generalization of compact spaces. A soft generalized topological space (F A , µ) is soft µ-compact if every soft µ-open soft cover of F A admits a finite soft sub cover. We characterize soft µ-compact space and study their basic properties.

2020

In this paper, based on the researches on soft set theory and soft topology, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Theorem to the class of soft topological spaces.

Computers & Mathematics with Applications, 2011

In the present paper we introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft T i-spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft T 1-space is also presented.

2019

In this paper, we introduce and study some new soft properties namely, soft R0 and soft R1(SRi, for short i = 0, 1) by using the concept of distinct soft points and we obtain some of their properties. We show how they relate to some soft separation axioms in [21]. Also we, show that the properties SR0, SR1 are special cases of soft regularity. We further, show that in the case of soft compact spaces, SR1 is equivalent to soft regularity. Finally, the relations between these properties in soft topologies and that in crisp topologies are studied. Moreover, some counterexamples are given.

JOURNAL OF ADVANCES IN MATHEMATICS

In the present paper, we have continued to study the properties of soft topological spaces. We introduce new types of soft compactness based on the soft ideal Ĩ in a soft topological space (X, τ, E) namely, soft αI-compactness, soft αI-Ĩ-compactness, soft α-Ĩ-compactness, soft α-closed, soft αI-closed, soft countably α-Ĩ-compactness and soft countably αI-Ĩ-compactness. Also, several of their topological properties are investigated. The behavior of these concepts under various types of soft functions has obtained

Science journal of University of Zakho, 2019

The objective of studing the current paper is to introduced a new class of soft open sets in soft topological spaces called soft "-open sets. Then soft "-open sets are used to study some soft topological concepts. Furthermore, the concept of soft "-continuous and almost soft "-continuous functions are defined by using the soft "-open sets. Some properties and Characterizations of such functions are given.

New Trends in Mathematical Science, 2016

In this paper, a new class of generalized soft open sets in soft generalized topological spaces as a generalization of compact spaces, called soft b-compact spaces, is introduced and studied. A soft generalized topological space is soft b-compact if every soft b-open soft cover of F E contains a finite soft subcover. We characterize soft b-compact space and study some of their basic properties.

In this Paper, we introduce a new definition of the cover so-called fuzzy soft p-cover. According to this notion, we define a new type of compactness in fuzzy soft topology so-called p *-compactness which is extension to Kandil's compactness in the fuzzy topology [7] and is avoid some Chang's deviations in the fuzzy and fuzzy soft topology [4]. Some of their basic results, properties and relations are investigated with some necessary examples.