B-open Sets Research Articles

Weak Soft Separation Axioms and Weak Soft (1,2)*-D ~ -Separation Axioms in Soft Bitopological Spaces

Abstract: In this article we introduce and study new types of soft sets in soft bitopological spaces, namely, soft (1,2)*-difference sets and soft (1,2)*-b-difference sets by using the notion of soft -open sets and soft (1,2)*-b-open sets respectively. Furthermore we use these soft sets to define and study new types of soft separation axioms, namely, soft (1,2)*- -spaces and soft (1,2)*-b- -spaces for which are weaker than soft (1,2)*- -spaces and soft (1,2)*-b- -spaces for respectively. The basic properties and characteristics each of soft (1,2)*-b- -spaces, soft (1,2)*- -spaces and soft (1,2)*-b- -spaces for also have been studied.

Separation Axioms and Graphs of Functions in Nano Topological Spaces via Nano $\beta$b-open Sets

Separation Axioms and Graphs of Functions in Nano Topological Spaces via Nano $\beta$b-open Sets

On b-Regularity and Normality In Intuitionistic Fuzzy Topological Spaces

In this paper using the concept of fuzzy b-open (fuzzy b-closed)sets to introduce some new types of intuitionistic fuzzy b separation axioms, intuitionistic fuzzy b-Ti space (for \(i = 3, 4\)) and (intuitionistic Fuzzy b-Regular and b-normal) spaces are introduced. Some theorems about them are investigated. Stronger forms of (intuitionistic fuzzy b-regular) and (intuitionistic fuzzy b-normal) spaces are introduced. Moreover, the relationships between these separation axioms and others are investigated.

Pairwise Generalized b-Ro Spaces in Bitopological Spaces

The main purpose of this paper is to introduce pairwise generalized b-Ro spaces in bitopological spaces with the help of generalized b-open sets in bitopological spaces and give several characterizations of this spaces. We also introduce generalized b-kernel of a set and investigate some properties of it and study the relationship between this space and other bitopological spaces.

γb-sets and γb-continuous functions

First of all we introduce a new class of sets is called γb-sets and a new type of continuous functions is called γb-continuous functions. Then, we investigate some properties and characterizations. Besides, γb-sets and γb-continuity are used to extend known results for b-open sets and b-continuity.

Comments on “Soft b-open sets and soft b-continuous functions, Math. Sci. (2014) 8:124”

Comments on “Soft b-open sets and soft b-continuous functions, Math. Sci. (2014) 8:124”

On Generalized Open Sets

We introduce and explore generalized open sets namely $\gamma$-pre-open and $\gamma$-b-open sets in topological spaces. We also explore and investigate the properties and characterizations of $\gamma$-b-continuous function, $\gamma$-b-irresolute function and $\gamma$-b-open(closed) functions. Examples and counter examples are also provided for the existence of defined concepts.

On G*B-Kernal in Topological Spaces

In this paper, we introduce G*B-K(A), WU-g*b-separated, N#g*b(x) and g*b-D by using g*b-open sets in topological spaces and study the characterizations and their properties.

Soft b-open sets and soft b-continuous functions

In this paper, a new class of generalized soft open sets in soft topological spaces, called soft b-open sets, is introduced and studied. Then discussed the relationships among soft α-open sets, soft semi-open sets, soft pre-open sets and soft β-open sets. We also investigated the concepts of soft b-open functions and soft b-continuous functions and discussed their relations with soft continuous and other weaker forms of soft continuous functions.

A Discourse on Analytical Study of Nearly - Open Sets

The aim of this paper is to elaborate the study of some nearly- open sets as p-open, s-open, α-open & β-open sets & the associated strongly continuity as well as compactness. Also the inter relationship of these nearly open sets has been discussed.

On some properties of generalized open sets in generalized topological spaces

Abstract In [8], Császár introduced some generalized open sets in generalized topological spaces, namely, μ-semi-open, μ-preopen, μ-β-open, and μ-α-open. The primary purpose of this paper is to study some new properties and characterizations of these concepts as we also introduce and study a new generalized open set in generalized topological spaces, namely, μ-b-open. We also investigate some relationships between these concepts.

On Bitopological γ-open sets

The purpose of this paper is to introduce and study the properties of (1,2) γopen set in bitopological space .In this paper we also study (1, 2) γ-locally closed set, (1,2) γ-t-set, (1,2) γ-B-set and relationship between (1,2) b-open set and (1,2) γ-open set . Keywords(1, 2) b-open set , (1,2) B-set, (1,2) t-set (1,2) locally closed , (1,2) γopen set .

Multi topological approximations of rough set theory

In this paper, we generalise Pawlak’s approximation spaces to topological approximation spaces. These topological approximation spaces are generated using many topological notions such as regular open sets, semi-open sets, pre-open sets, γ-open sets, α-open sets and β-open sets and others. The basic definitions and properties of these topological approximation spaces are introduced and sufficiently illustrated. We put all topological generalisations in one generalisation called m-generalisation spaces.

Bc-Open Sets in Topological Spaces

In this paper, we introduce a new class of b-open sets called Bc-open, this class of sets lies strictly between the classes of θ-semi open and b-open sets. We also study its fundamental properties and compare it with some other types of sets and we investigate further topological properties of sets and we introduce and investigate new class of space named Bc-compact.

On regular b-open sets in topological spaces

On regular b-open sets in topological spaces

On b-connectedness and b-disconnectedness and their applications

In this paper, by using b-open (=c-open) sets we study the concept of b-separated sets. With this concept we study the notion of b-connected sets and strongly b-connected sets. We give some properties of such concepts with some b-separation axioms and compact spaces. Finally, we construct a new topological space on a connected graph.

Operation approaches on b-open sets and applications

In this paper, we introduce the concept of an operation gamma on a family of b-open sets in a topological space (X,tau). Using this operation gamma, we introduce the concept of b-open sets and study some of their properties.

Fuzzy b- Compact and Fuzzy b-closed Spaces

form of fuzzy compact spaces namely fuzzy bc ompact spaces ,bclosed spaces and fbgcompact spaces wi th the concept of fuzzy bopen set are introduced.Some characterization on their properties are obtained.The invariance of fuzzy bcompact spaces, bclosed spac es and fbgcompact spaces under fuzzy mapping and their h eriditary property are also investigated.

β-Approach to near set theory

The aim of this paper is to introduce two approaches to near sets by using topological structures and β-open sets. Some fundamental properties and characterizations are given. We obtain a comparison between these types of approximations and the approximation introduced by J.F. Peters.

ON BI-METACOMPACT SPACES

The primary purpose of this paper is to introduce and study new variations of metacompactness by utilizing b-open sets.