Annals of Communications in Mathematics

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.

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

ABSTRACT.In this article, we focus on nano \( \mathcal{S} \)-closed sets and nano \( \mathcal{S}_{\delta} \)-closed sets are introduced and study. Also, we introduce and study nano \( \mathcal{S} \)-continuous functions and nano \( \mathcal{S}_{\delta} \)-continuous functions. Furthermore, we introduce the notions of nano topological spaces called nano \( \mathcal{S}\text{-}T_{1/2} \) space and nano \( \mathcal{S}\text{-}T_{5} \) space.

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.