The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

In this paper, we first study the species of finite topological spaces recently considered by Fauvet, Foissy, and Manchon. Then, construct a twisted pre-Lie structure on connected spaces. The underlying defines coproduct different from those already defined authors above. end, illustrate link between Grossman–Larson product proposed coproduct.

We carefully define and study C∗-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology along the way. We explain the triangulated category structure on the bivariant Kasparov theory over a topological space and study the analogue of the bootstrap class for C∗-algebras over a finite topological space.

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...

In [5], a representation of bounded lattices within so-called standard topological contexts has been developed. Based on the theory of formal concept analysis [14] it includes Stone’s representation of Boolean algebras by totally disconnected compact spaces [10], Priestley’s representation of bounded distributive lattices by totally order disconnected compact spaces [7] as well as Urquhardt’s r...

The aim of the present paper is to define and study (IC)$LM$-fuzzytopological spaces, a generalization of (weakly) induced $LM$-fuzzytopological spaces. We discuss the basic properties of(IC)$LM$-fuzzy topological spaces, and introduce the notions ofinterior (IC)-fication and exterior (IC)-fication of $LM$-fuzzytopologies and prove that {bf ICLM-FTop} (the category of(IC)$LM$-fuzzy topological ...

The purpose of this paper is to construct the concept of semi$theta$-compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$-compactness and locally semi -compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.