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 paper, the new grill notions are studied using grill topological spaces and by using some defined sets where the sets Gt-set and GR-set are defined. Properties of this set and some relationships are investigated and deal with a grill topological spaces.

ABSTRACT.In this study, we investigate specific kernel structures within interval valued topological spaces. We introduce the notions of interval-valued Λ-sets and interval-valued λ-closed sets and discuss their essential properties. The connections between these concepts and existing notions in interval-valued topology are examined in detail. Various characterizations and foundational results are presented to clarify their structural behavior. This work aims to enhance and extend the theoretical framework of interval-valued topology.