Soft elementary compact in soft elementary topology
Mahmoud Bousselsal2018, arXiv (Cornell University)
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
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.
Related papers
On elementary soft compact topological spaces
MANAS Journal of Engineering, 2021
This paper is a work on elementary soft (𝜖-soft) compact spaces. We first define the cofinite 𝜖-soft compact space and prove that the image of an 𝜖-soft compact space under a soft continuousmapping is 𝜖-soft compact space. We then examine the relationship between 𝜖-soft compactspace and classical compact space and give an illustrative example.
Soft topology redefined
arXiv: General Mathematics, 2016
In this paper we give a new definition of soft topology using elementary union and elementary intersection although these operations are not distributive. Also we have shown that this soft topology is different from Naz's soft topology and studied some basic properties of this new type of soft topology. Here we use elementary complement of soft sets, though law of excluded middle is not valid in general for this type of complementation.
On topological soft sets
Journal of Applied Mathematics, Statistics and Informatics, 2020
In this paper, we have established topological soft sets over generalized topological spaces and topological spaces, and studied its structural properties. We have derived a topological soft set in any given topological space, and from this point of view, we have given necessary and sufficient condition for homeomorphic Alexandroff spaces using topological soft set technique. At last, we have derived a topological soft set using closed sets in any topological space and we have given necessary and sufficient condition for arbitrary homeomorphic topological spaces using them.
Countable and separable elementary soft topological space
Mathematical Methods in the Applied Sciences, 2020
This paper is an introduction to countable and separable elementary soft topological spaces, which includes concepts such as dense soft set, first countability, second countability, separability and Lindelöf properties and some basic properties of them in the elementary soft topological spaces.
Some Properties of Soft Β-Compact and Related Soft Topological Spaces
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.
On Soft $\mu$-Compact Soft Generalized 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.
A Soft Embedding Theorem for Soft Topological Spaces
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.
On soft πgb-closed sets in soft topological spaces
2015
This paper focuses on soft $\pi$gb-closed sets and soft $\pi$gb-open sets in soft topological spaces and to investigate its properties. Further soft $\pi$gb-T1/2 space is introduced and its basic properties are discussed.
On 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.
On Compactness in Fuzzy Soft Topological Spaces
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.
Related topics
Related papers
Soft Topology Generated by L-Soft Sets
2018
In this paper, the theory of soft topological space generated by L-soft sets is in troduced. As a continuation of the study of operations on L-soft sets, the aim of this paper is to introduce new soft topologies using restricted and extended intersections on L-soft sets and to study the diferences of these soft topologies.
Introduction To Maximal Soft e-Open (Minimal Soft e-Closed) Sets in Soft Topological spaces
2017
Recently, the authors [17] introduced the notions of soft e-open sets and soft e-continuity in soft topological spaces. In this paper, a new class of soft sets called maximal soft e-open sets and minimal soft e-closed sets which are fundamental results for further research are defined on soft topological space and continued in investigating the properties of these new notions of open sets with example and counter examples. 2010 AMS CLASSIFICATIN: 54A10, 54A05 and 06D72 Key Words: Soft regular open sets, soft regular closed sets, soft e-cluster point, soft e-open sets, soft e-closed sets, soft -semi-maximal open sets, soft -semi-minimal closed sets etc.
Soft b-compact spaces
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.
Some new properties on soft topological spaces
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.
On Soft bc-Open Sets in Soft Topological Spaces
Iraqi Journal of Science, 2020
In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Ƅc-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Ƅ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets.
Some generalized forms of soft compactness and soft Lindelöfness via soft α-open sets
2020
By using a notion of soft α-open sets, we generalize the concepts of soft compact and soft Lindelöf spaces. We define the concepts of soft α-compact, soft αLindelöf, almost (approximately, mildly) soft α-compact and almost (approximately, mildly) soft α-Lindelöf spaces. We present two new kinds of the finite intersection property and utilize them to characterize almost soft α-compact and approximately soft α-compact spaces. To elucidate the relationships among the introduced spaces and to illustrate our main results, we supply several interesting examples. Also, we point out that the initiated spaces are preserved under soft α-irresolute mappings and we investigate certain of results which associate an extended soft topology with the introduced soft spaces. In the end, we conclude some findings which associate the introduced spaces with some soft topological notions such as soft α-connectedness, soft α-T2-spaces, soft α-partition and soft subspaces. ∗. Corresponding author SOME GENE...
Soft Generalized Closed Sets in Soft Topological Spaces
In the present paper, we introduce soft generalized closed sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters. A sufficient condition for a soft g-closed set to be a soft closed is also presented. Moreover, the union and intersection of two soft g-closed sets are discussed. Finally, the new soft separation axiom, namely soft 1 2 T -space is introduced and its basic properties are investigated.
Methodological remarks on soft topology
Soft Computing, 2021
The paper points out the methodological aspects of soft topological spaces which are defined over an initial universe set U with a fixed set of parameters E. The basic change of view is due to the fact that soft topology is actually a topology on the product of two sets, and in many cases, standard methods of general topology can be applied. Furthermore, in many papers some notions are introduced by different ways and it would be good to give a unified approach for a transfer of topological notions to a soft set theory and to create a bridge between general topology and soft set theory. On the other hand, not all counterparts of soft concepts are studied on classical topology and some types of separation axioms support this fact.
On Soft Topological Space via Semiopen and Semiclosed Soft Sets
Kyungpook mathematical journal, 2014
This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi interior and semi closure of a soft set in a soft topological space. Various forms of soft functions, like semicontinuous, irresolute, semiopen soft functions are introduced and characterized. Further soft semicompactness, soft semiconnectedness and soft semiseparation axioms are introduced and studied.
Soft ξ-open sets in Soft Topological Spaces
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.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.