The purpose of this paper is to establish the compactness in intuitionistic fuzzy topological space. In this paper we give four new notionsof separation axioms and one notions of locally compactness in intuitionistic fuzzy topological space. Also, we discuss separation axioms in intuitionistic fuzzy compactness and some of its features. Further, we investigate the behavior of intuitionistic fuzzy compactness under several types of fuzzy separation axioms.Keywords: Fuzzy set, intuitionistic fuzzy set, intuitionistic topological space, intuitionistic fuzzy topological space, intuitionistic fuzzy compactness, intuitionistic fuzzy hausdorff space.

The purpose of this paper is to introduce and study the compactness in intuitionistic fuzzy topological spaces. Here we define two new notions of intuitionistic fuzzy compactness in intuitionistic fuzzy topological space and find their relation. Also we find the relationship between intuitionistic general compactness and intuitionistic fuzzy compactness. Here we see that our notions satisfy hereditary and productive property. Finally we observe that our notions preserve under one-one, onto and continuous mapping.

The purpose of this paper is to establish the connectedness in intuitionistic fuzzy topological space. In this paper we give six notions of separatedness, connectedness and total connectedness and one notion of T1-space in intuitionistic fuzzy topological space. Also, we find a relation between classical topology and intuitionistic fuzzy topology. Further, we show that connectedness in intuitionistic fuzzy topological spaces are productive and we demonstrate some of its features.

The purpose of this paper is to give some new notions of intuitionistic fuzzy regular spaces and investigate the relationship among them. Also the relations between our notions and other given notion of intuitionistic fuzzy regular spaces have been investigated. Moreover it is shown that all these notions satisfy hereditary property of regular spaces. Finally it is shown that under some conditions image and preimage preserve intuitionistic fuzzy regular spaces.

The aim of this paper is to establish the (r, s)-connectedness in intuitionistic fuzzy topological space. Here we give two new notions of (r, s)-connectedness and total (r, s)-connectedness in intuitionistic fuzzy topological space. Also, we find a relation about classical topology and intuitionistic fuzzy topology. Furthermore, using some provisos we will show that (r, s)-connectedness in intuitionistic fuzzy topological spaces are productive and some of its features.