$\alpha$-Topological Vector Spaces

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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