Separation axioms via ${ }^{\star} \delta$-set in topological vector spaces

Abstract

In this paper we introduce a new sort of spaces as ${ }^{\star} \delta$-Homogenous space, ${ }^{\star} \delta$-Hausdorff space and ${ }^{\star} \delta$ Compact space. It provides a new connection between ${ }^{\star} \delta$-Vector spaces and ${ }^{\star} \delta$-homogenous spaces. Also we investigated the relationship between the translation and scalar multiplication mappings and $\star \delta$-homeomorphism on ${ }^{\star} \delta$-Topological vector spaces. Finally we derive ${ }^{\star} \delta$-Topological vector space is ${ }^{\star} \delta$-Hausdorff and ${ }^{\star} \delta$-Compact spaces.is