Α-open Sets Research Articles

On Fuzzy Soft α-open Sets, α-continuity, andα-compactness: Some Novel Results

In this paper, we defined the notions of fuzzy soft α-interior (α-closure) operators via fuzzy soft topologies based on the sense of Sostak and studied some topological properties of them. Also, the notion of r-fuzzy soft α-connected sets was introduced and investigated. Thereafter, we defined and characterized the notions of fuzzy soft weakly (almost) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings. Moreover, we established that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. In addition, we investigated some properties of fuzzy soft α-continuity. It is also we showed that the composition is fuzzy soft almost α-continuous mapping if is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some novel types of fuzzy soft compactness via r-fuzzy soft α-open sets were introduced and the relationships between them were explored with the help of some examples.

On Gα -open sets

The new concepts in grill topological spaces are investigated in this study by employing specified sets in which the α-open sets are defined and grill topological spaces. Properties of this set and certain relationships are studied, examining a group of functions, like open, closed, and continuous functions, determining their relation with each other and giving examples and properties associated with this set. This shall serve as the beginning of examining numerous topological properties with this set.

Between the Classes of Soft Open Sets and Soft Omega Open Sets

In this paper, we define the class of soft ω0-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of a given soft anti-locally countable soft topological space and the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of the soft topological space of soft ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.

Ii- Open Set in Bitopological Spaces

In this paper, we define ii-open set in bitopological space as follows: Let ( , , ) be a bitopological space, a subset A of is said to be ( – ii- open set ) if there exist U,V ≠ and U,V such that: A=int1(U) or A=int2 (V) A or A We study some characterizations and properties of this class. Also, we explain the relation between ii- open sets and open sets, i-open sets and α-open sets in bitopological space. Furthermore, we define ii- continuous mapping on bitopological spaces with some properties.

Soft ii-Open Sets in Soft Topological Spaces

In the current study, researchers have introduced modern concepts of soft open sets in the spaces of soft topologies named as soft i-open, soft inter-open and soft ii-open sets and they have explained the relations between these concepts and some other concepts such as the soft semi-open and soft α-open sets. They have also used a definition of soft open neighborhood of a point in X to introduce and discuss some applications of soft ii-open sets as soft ii-closure, soft ii-interior, soft ii-exterior, soft ii-border and soft ii-frontier of the soft set. Finally, they gave an example to explain and clarify all mentioned applications.

Topological Group Via Operations defined on α-Open Sets

Topological Group Via Operations defined on α-Open Sets

α-Topological Vector Spaces

The main objective of this paper is to present the study of α-topological vector spaces. α-topological vector spaces are defined by using α-open sets and α-irresolute mappings. Notions of convex, balanced and bounded set are introduced and studied for α-topological vector spaces. Along with other results, it is proved that every α-open subspace of an α-topological vector space is an α-topological vector space. A homomorphism between α-topological vector spaces is α-irresolute if it is α-irresolute at the identity element. In α-topological vector spaces, the scalar multiple of α-compact set is α-compact and αCl(C) as well as αInt(C) is convex if C is convex. And also, in α-topological vector spaces, αCl(E) is balanced (resp. bounded) if E is balanced (resp. bounded), but αInt(E) is balanced if E is balanced and 0 ∈ αInt(E).

UTILIZING SUPRA α-OPEN SETS TO GENERATE NEW TYPES OF SUPRA COMPACT AND SUPRA LINDELÖF SPACES

The purpose of this article is to introduce the concepts of supra α-compact(supra α-Lindel¨of) spaces, almost supra α-compact (almost supra α-Lindel¨of) spaces and mildly supra α-compact (mildly supra α-Lindel¨of) spaces in supra topological spaces utilizing a notion of supra α-open sets. Several properties of each concept are established and the relationships among them are provided with the help of interesting examples. A notion of supra α-limit points is presented and some properties with supra α-compactness are derived.

Some New Functions Via Operations defined on α-Open Sets

Some New Functions Via Operations defined on α-Open Sets

α-ℽ-convergence, α-ℽ- accumulation and α-ℽ- compactness

The aim of the present paper is to introduce the concept of α-ℽ compactness by means of -operation defined on the family of α-open sets of a topological space. We define the α-ℽconvergence,α-ℽaccumulation points of a filterbase and give some of their properties. Some characterizations and properties of α-ℽ-compact spaces are obtained.

Some applications of Dα-closed sets in topological spaces

In this paper, a new kind of sets called Dα-open sets are introduced and studied in a topological spaces. The class of all Dα-open sets is strictly between the class of all α-open sets and g-open sets. Also, as applications we introduce and study Dα-continuous, Dα-open, and Dα-closed functions between topological spaces. Finally, some properties of Dα-closed and strongly Dα-closed graphs are investigated.

Semi-Star-Alpha-Open Sets and Associated Functions

The aim of this paper is to introduce vari- ous functions associated with semi*α-open sets. Here semi*α- continuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characteriza- tions for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are intro- duced and their properties are studied. In addition strongly semi*α-irresolute functions, contra-strongly semi*α-irresolute functions, semi*α-totally continuous, totally semi*α- continuous functions and semi*α-homeomorphisms are intro- duced and their properties are investigated. General Terms: General topology

English

In this paper, we introduce new concepts, namely semi*α-connectedness and semi*α- compactness using semi*α-open sets. We investigate their basic properties. We also discuss their relationships with already existing concepts of connectedness and compactness. Mathematics Subject Classification: 54D05, 54D30.

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.

Softα-Open Sets and Softα-Continuous Functions

We introduce softα-sets on soft topological spaces and study some of their properties. We also investigate the concepts of softα-continuous and softα-open functions and discuss their relationships with soft continuous and other weaker forms of soft continuous functions. Also counterexamples are given to show the noncoincidence of these functions.Corrigendum to “Soft α-Open Sets and Soft α-Continuous Functions”

Locally α-compact spaces based on continuous valued logic

Abstract This paper is a continuation of [1] . That is, it considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [2] . It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). Other characterizations of fuzzifying α-compactness are given, including characterizations in terms of nets and α-subbases. Several characterizations of locally α-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

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.

ON OPERATION APPROACHES OF α-OPEN SETS AND SEMI-OPEN SETS

ON OPERATION APPROACHES OF α-OPEN SETS AND SEMI-OPEN SETS

On ultra α-countable dense homogeneous spaces

The aim of this paper is to introduce the countable dense homogeneous spaces in bitopological spaces based on (1, 2)α-open sets.

On fuzzy almost compact spaces

In this article, an investigation of almost compactness for fuzzy topological spaces including certain new characterizations is attempted in terms of fuzzy Θ c-sets, α-open sets, α-closure operator, Θ-open sets and C Θ -accumulation points.