$\alpha$-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.