A New type of Connected Sets via Bioperations

The purpose of this paper is to introduce the notion of $\alpha_{(\gamma, \gamma^{'})}$-separated sets and study their properties in topological spaces, then we introduce the notions of $\alpha_{(\gamma, \gamma^{'})}$-connected and $\alpha_{(\gamma, \gamma^{'})}$-disconnected sets. We discuss the characterizations and properties of $\alpha_{(\gamma, \gamma^{'})}$-connected sets and then properties under $(\alpha_{(\gamma, \gamma^{'})}$, $\alpha_{(\beta, \beta^{'})})$-continuous functions. The $\alpha_{(\gamma, \gamma^{'})}$-components in a space $X$ is also introduced

On Pre-γ-I-Open Sets In Ideal Topological Spaces

In this paper, we introduce and study the notion of pre-γ-I-open sets in ideal topological space

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)

A New Type of Weakly Commutative Groups

The aim of the present paper is to define and study a new class of groups, namely Wm-groups with a single binary operation based on axioms of semi commutativity, right identity and left inverse. Moreover, we introduce the notions of right cosets, quotient Wm-groups, homomorphisms, kernel and normal Wm-subgroups in terms of Wm-groups, and investigate some of their properties

On alpha_(gamma, gamma^')-Separation Axioms

The purpose of this paper is to introduce and study new separation axioms by using the notions of $\alpha$-open and $\alpha$-bioperations. Also, we analyze the relations with some well known separation axioms

A New type of Connected Sets via Bioperations

The purpose of this paper is to introduce the notion of $\alpha_{(\gamma, \gamma^{'})}$-separated sets and study their properties in topological spaces, then we introduce the notions of $\alpha_{(\gamma, \gamma^{'})}$-connected and $\alpha_{(\gamma, \gamma^{'})}$-disconnected sets. We discuss the characterizations and properties of $\alpha_{(\gamma, \gamma^{'})}$-connected sets and then properties under $(\alpha_{(\gamma, \gamma^{'})}$, $\alpha_{(\beta, \beta^{'})})$-continuous functions. The $\alpha_{(\gamma, \gamma^{'})}$-components in a space $X$ is also introduced

Micro Separation Axioms

In this paper, some new types of spaces are defined and studied in micro topological spaces namely, Micro T0, Micro T1, Micro T2, Micro R0 and Micro R1 spaces. Properties and the relationships of these spaces are introduced. Finally, the relationships between these spaces and the related concepts are investigated

On alpha_(gamma, gamma^')-Separation Axioms

The purpose of this paper is to introduce and study new separation axioms by using the notions of $\alpha$-open and $\alpha$-bioperations. Also, we analyze the relations with some well known separation axioms