On Almost $\alpha$-Topological Vector Spaces

Abstract

The main objective of this paper is to introduce a new generalized form of topological vector spaces, namely, almost $\alpha$-topological vector spaces by using the concepts of $\alpha$-open sets, regular open sets, and almost $\alpha$-continuous mappings. In the present paper, some important examples of almost $\alpha$-topological vector spaces with basic properties are characterized.