New results on soft generalized 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.

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.

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.

gazi university journal of science, 2014

Arockiarani and Lancy (7), defined soft preopen (c losed) sets on soft topology. In this paper, we are continue investigating the properties of soft preopen (clos ed) sets and define soft preclosure and soft preinterior in soft topological spaces. We are also introduce and research basic properties of the concepts of soft prere gular spaces, soft P ₃�spaces, soft prenormal spaces and soft P ₄�spaces in soft topological spaces, which are basic for further research on soft topology and will fortify the footing of the theory of soft topological space.

2015

Many scientists have studied and improved the soft set theory, which is initiated by Molodtsov (33) and easily applied to many problems having uncertainties from social life. The main purpose of our paper, is to introduce new soft separation axioms based on the b-open soft sets which are more general than of the open soft sets. We show that, the properties of soft b-Ti-spaces (i = 1, 2) are soft topological properties under the bijection and irr esolute open soft mapping. Also, the property of being soft b-regular and soft b-normal are soft topological properties under bijection, irresolute soft and irresolute open soft functions. Furthe r, we show that the properties of being soft b-Ti-spaces (i = 1, 2, 3, 4) are hereditary properties.

International Journal of Mathematics Trends and Technology, 2016

In this paper we introduce four new sets namely soft αμ -closed sets, soft gα μ -closed sets, soft *gα μ closed sets, soft β*gα μ-closed sets in Soft Generalized Topological Spaces and derive their relationship. By using soft β*gα μ -closed sets, we introduce some seperation axioms and investigate their properties with the help of continuity and irresoluteness in Soft Generalized Topological Spaces (SGTS).

The aim of this study is to introduce and investigate two new classes of separation axioms called supra soft R 0 and supra soft R 1. They are defined in the spaces of supra soft topologies by using the notions of supra soft open sets and supra soft closure operator. We discuss the basic properties and characterizations of them. We also study the relationships between these classes and some other supra soft separation axioms with many results and explanative examples. Moreover, the connections between the properties of these classes and those in some generated soft topologies are presented. Finally, we show that these classes are preserved under subspaces, which means they are supra soft topological properties.

Malaya Journal of Matematik,, 2019

The main objective of this article is to introduce soft generalized separation axioms in soft bi topological spaces relative to crisp points and soft points. Further we will address the behavior of soft semi T 3 and soft normal semi T 4 spaces at different angles with respect to ordinary points as well as with respect to soft points. Hereditary properties are also discussed. Keywords Soft sets, soft points,soft topology,soft bi topological space,soft semi open set, soft semi T i spaces(i=1,2,3,4), soft semi regular and soft semi normal spaces.

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.

Journal of new theory, 2017

this paper, a new class of generalized soft open sets in soft topological spaces, called soft e-open set is focused and investigated some properties of them. Then focused the relationships among soft δ-pre open sets, soft δ-semi open sets, soft pre-open sets and soft e-open sets. We also investigated the concepts of soft e-open functions, soft e-continuous, soft e-irresolute and soft e-homeomorphism on soft topological space and discussed their relations with existing soft continuous and other weaker forms of soft continuous functions. Further soft e-separation axioms have been introduced and investigated with the help of soft e-open sets. Finally, we observed that the collection Ser-h(X,τ,E) form a soft group.