Micro P_β- Open Set in Micro Topological Spaces

Abstract

    This paper introduces a new class of open sets within micro topological spaces, termed Micro -open sets. We investigate its fundamental properties. Furthermore, we establish the exact inclusion relations, proving that any Micro -open set is necessarily Micro pre-open, Micro -open, and Micro  -open. Through counterexamples, we demonstrate that these inclusions are not reversible and that the class of Micro -open sets is independent of Micro -open, Micro semi-open, Micro -open and Micro  -open sets.