$\alpha$-Topological Vector Spaces

Year 2018, Volume: 47 Issue: 5, 1102 - 1107, 16.10.2018

Talal Al-hawary

Abstract

The notion of $\alpha$-topological vector space is introduced and several properties are studied. A complete comparison between this class and the class of topological vector spaces is presented. In particular, $\alpha$-topological vector spaces are shown to be independent from topological vector spaces. Finally, a sufficient condition for $\alpha$-regularity of $\alpha$-topological vector spaces is given.

Keywords

$\alpha$-open set, $\alpha$-irresolute map, $\alpha$-topological vector space

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