2017-04

Second International Scientific Conference-University of Zakho: ’Zakho: Life, Civilization, and Culture’

(1. 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).) (2. 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.)

2016-08

Second International Conference of The College of Education, The University of Garmian: ’Toward Further Progress in The Science of Mathematics (Theoretical and Practical)

The main purpose of the present paper is to define and study the notions of new classes of functions, namely $\alpha$-$\beta$-continuous, $\alpha$-$\beta$-closed graph, $\alpha$-($\gamma$, $\beta)$-continuous, $\alpha$-($\gamma$, $\beta)$-homeomorphic, $\alpha_{(\gamma, \beta)}$-open functions, and to give some properties of these functions in topological spaces.

2016-07

The 1st International Conference of Natural Science

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

2013-04

The 1st International Scientific Conference

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