Annals of Communications in Mathematics

ABSTRACT.In this paper, we study functions between domain \( \zeta \)-nano topological spaces and codomain nano topological spaces, which means every nano topology has its inverse image in \( \zeta \)-nano topology (i.e., \( \zeta \)-continuous). We establish the \( \zeta \)-cluster point in \( \zeta \)-continuous. We search image from a \( \zeta \)-open set (\( \zeta \)-closed set) to a nano open set (nano closed set) is called a \( \zeta \)-open map (\( \zeta \)-closed map). Finally, some of the results are portrayed with these \( \zeta \)-continuity with \( \mathcal{N} \)-continuity and we extend to \( \zeta \)-homeomorphism.

AbstractAim of this article, Rajasekaran [11] introduced strongly pre-I-open sets and in nano topological spaces. The relationships of strongly pre-nI-open sets with various other nano RI -set and nano I-locally closed sets are investigated.

AbstractWe introduce the notions of nano L*-perfect, nano R*-perfect, and nano C*-perfect sets in ideal nano spaces and study their properties. We obtained a characterization for compatible ideals via nano R*-perfect sets and and investigate further their important properties