α-Topological Vector Spaces

Science Journal of University of Zakho

卷:5

Hariwan Z. Ibrahim¹ 

[1] University of Zakho;

关键词: α-Topological vector space;    α-open set;    α-irresolute mapping;    left (right) translation;    α-homeomorphism;   

DOI  :  10.25271/2017.5.1.310

来源: DOAJ

【 摘 要 】

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).

【 授权许可】

Unknown