This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $...

We introduce r -fuzzy strongly preopen and r -fuzzy strongly preclosed sets in fuzzy topological space in view of the definition of Šostak (1985). We investigate some properties of them. Moreover, the concepts of fuzzy SP-continuous, fuzzy SP-irresolute continuous, fuzzy SP-irresolute open (closed) mappings, and a fuzzy SP-irresolute homeomorphism are introduced and studied. Some of their chara...

In this paper we introduce the gradation of separation axioms ST 0 , RT 0 in an intuitionistic fuzzy topological space in the sense of Mondal and Samanta [7]. Using these concepts we have introduced and studied α-and α *-RT 0 intuitionistic fuzzy topological spaces.

We introduce the notion of (r,s)-connected sets in intuitionistic fuzzy topological spaces and investigate some properties of them. In particular, we show that every (r,s)-component in an intuitionistic fuzzy topological space is (r,s)-component in the stratification of it.

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

The concept of fuzzy topological spaces was introduced in [2] and ever since this introduction much research has been done in this area. In this note we introduce the concept of extension of fuzzy topological spaces as done for topological spaces in [1,7]. Let (X, T) be a fuzzy topological space and T C T*. Then T* will be called a simple extension of T iff there exists a 6 $T such that T* = {A...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Using a gradation of openness in a (Chang fuzzy) I-topological space, we introduce degrees of compactness that we call α-fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α-locally compact spaces and construct a one-point α-fuzzy compactification of an I-topological space. 1. Introduction....

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

In this paper a new type of fuzzy multifunction termed as δ-precontinuous fuzzy multifunction has been introduced and studied. Some characterizations and several properties of this multifunction are obtained. We also characterize this multifunction by newly define fuzzy neighbourhood of a fuzzy set in a fuzzy topological space. Finally, in the last section some applications of this fuzzy multif...