Analysis of $ T_{1} $ separation axioms within extended fuzzy topological frameworks

Abstract

In this paper, we introduce new definitions of extended fuzzy $T_{1}$ spaces and establish relations between them and their counterparts. We show that these concepts have projective, productive, and hereditary characteristics. We also demonstrate that generalized bijective fuzzy continuous and generalized fuzzy open mappings preserve these spaces. Furthermore, these ideas are examined in the framework of initial and final extended fuzzy topological spaces.