Science Journal of University of Zakho | 卷:5 |
α-Topological Vector Spaces | |
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