α-Topological Vector Spaces

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).

Keywords

• α-Topological vector space
• α-open set
• α-irresolute mapping
• left (right) translation
• α-homeomorphism