Intuitionistic -Open Sets in Intuitionistic Topological Spaces

Abstract

This paper introduces a fresh direction of open sets in intuitionistic topological spaces (ITS), described as intuitionistic δ^⋆-open sets. The proposed class is described by using the intuitionistic δ-interior operator together with the ordinary intuitionistic interior and closure operators. The main aim is to construct a class that contains intuitionistic δ-open sets and gives a flexible structure for studying generalized interior, closure, exterior, boundary, and limit points. The paper presents the basic definitions of intuitionistic sets (IOS) and ITSs, defines the proposed class, proves its fundamental properties, and gives finite examples showing that the fresh direction is wider than the classical intuitionistic open class. The results show that the family of intuitionistic δ^⋆-open sets is stable under arbitrary unions and supports well-defined derived operators. These operators provide a systematic framework for future extensions of continuity, compactness, and separation axioms in ITS.