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.

Abstract:This paper presents the notion of ideal leras topological spaces as an extension of leras topological spaces. The connections between these two classes of spaces are examined in detail. Different forms of closed sets arising in ideal leras topological spaces are introduced and their interrelations are discussed. Several characterizations and fundamental properties associated with these sets are obtained. Examples are included to clarify the introduce concepts and the corresponding results.

Abstract: The purpose of this paper is to extend the study of generalized closed sets in leras topological spaces to the ideal setting. Using the leras local function and leras \( \star \)-closure operator associated with an ideal, we introduce and investigate two new classes of sets, called \( ideal\ leras\ generalized\ closed\ sets \) (\( I_{lrg} \)-closed sets) and \( ideal\ leras\ generalized\ open\ sets \) (\( I_{lrg} \)-open sets), in ideal leras topological spaces. We show that every \( lrg \)-closed set is \( I_{lrg} \)-closed, and that every \( I^\star \)-closed set is \( I_{lrg} \)-closed, while the converses fail in general, thereby placing the new classes correctly within the existing hierarchy of sets in leras and ideal leras topological spaces. Several characterizations of \( I_{lrg} \)-closed sets are obtained, including formulations in terms of the leras \( \star \)-closure operator, the leras closures of singletons, and the non-existence of nonempty \( Ir \)-closed sets in certain associated difference sets. Additional properties, such as finite unions of \( I_{lrg} \)-closed sets being \( I_{lrg} \)-closed and sufficient conditions under which \( I_{lrg} \)-closed sets coincide with \( lrg \)-closed sets, are also established. Appropriate examples are constructed throughout to illustrate the developed concepts and to demonstrate that the implications obtained cannot, in general, be reversed.