Nano Z Seperation Axioms

Abstract

AbstractBased on nano Z open set, we discuss and study about separation axioms, connectedness and compactness in a nano topological spaces. In this paper, the types of separation axioms such as \(\mathfrak {N} Z T_0\), \(\mathfrak {N} Z T_1\) and \(\mathfrak {N} Z T_2\) spaces are introduced and discuss in nano topological spaces. Also, nano Z regular space and nano Z normal space of nano Z open sets are established in nano topological spaces. Finally, nano Z compactness and nano Z connectedness are study and dealt with some properties in nano topological spaces.Keywords \(\mathfrak {N} Z T_0\) \(\mathfrak {N} Z T_1\) \(\mathfrak {N} Z T_2\) \(\mathfrak {N} Z reg\) \(\mathfrak {N} Z nor\) spacesnano Z compactnessnano Z connectednessAMS (2000) subject classification:54A0554A4054B05