Pre-Hausdorff and Hausdorff Objects in the Category of Quantale-Valued Closure Spaces

Epimorphisms in the Category of Hausdorff Fuzzy Topological Spaces

In this paper we have characterized the epimorphisms in the full subcategory of Hausdorff fuzzy topological spaces (introduced by Srivastava et al.[10]) of the category FTS of fuzzy topological spaces and fuzzy continuous functions using the Salbanytype closure operator.

Extensions of Hausdorff Spaces

QUANTALE-VALUED GAUGE SPACES

We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the qu...

Modal compact Hausdorff spaces

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

On soft Hausdorff spaces

The aim of this paper is to study some properties of soft Hausdorff space introduced by Shabir and Naz. Firstly, we give a representation of soft sets and soft topological spaces. Secondly, we introduce some new concepts in soft topological space such as convergence of sequences, homeomorphism and investigate the relations between these concepts and Hausdorff axiom in soft topological space. 20...