α-Topological Vector Spaces

  • Hariwan Z. Ibrahim University of Zakho
Keywords: α-Topological vector space, α-open set, α-irresolute mapping, left (right) translation, α-homeomorphism

Abstract

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).

Author Biography

Hariwan Z. Ibrahim, University of Zakho

Dept. of Mathematics, Faculty of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

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Published
2017-03-30
How to Cite
Ibrahim, H. (2017). α-Topological Vector Spaces. Science Journal of University of Zakho, 5(1), 107-111. https://doi.org/10.25271/2017.5.1.310
Section
Science Journal of University of Zakho