ON hα-IRRESOLUTE TOPOLOGICAL VECTOR SPACES

In this paper, we defined and investigated a generalized type of topological vector space known as $h\alpha$-irresolute topological vector spaces by using the notion of $h\alpha$-open sets, which was given by Abdullah et al. \cite{8} in 2022. We explore and investigate several properties and characterizations of this new notion of $h\alpha$-irresolute topological vector space. Also we give the several characterizations of $h\alpha$-compact space and $h\alpha$-Hausdorff space. Furthermore, we show that an $h\alpha$-irresolute topological vector space is $h\alpha$-hausdorff iff one-point set in $\mathcal{X}$ is $h\alpha$-closed in $\mathcal{X}$.