In this article on fuzzy topological spaces we studied and the further investigated different kind of continues mappings in fuzzy topological space. In this article fuzzy sets have been defined and use of fuzzy numbers in daily life. In this article we have investigated how the fuzzy topological spaces have been defined by different authors and what is its future scope.

in this paper, we introduce and characterize fuzzy wea-kly $e$-closed functions in fuzzy topological spaces and the relationship between these mappings and some properties of them are investigated.

following the idea of $l$-fuzzy neighborhood system as introduced byfu-gui shi, and its generalization to $(l,m)$-fuzzy neighborhood system, the relationship between  $(l,m)$-fuzzy topology and $(l,m)$-fuzzy neighborhood system will be further studied. as an application of the obtained results, we will describe the initial structures of $(l,m)$-fuzzy neighborhood subspaces and $(l,m)$-fuzzy top...

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces.

The fuzzy concept has invaded all branches of Mathematics ever since the introduction of fuzzy set by Zadeh [10]. Fuzzy sets have applications in many fields such as information [5] and control [8]. The theory of fuzzy topological spaces was introduced and developed by Chang [3] and since then various notions in classical topology have been extended to fuzzy topological spaces. Sostak [6] intro...

Topological relations are one of the most fundamental properties between spatial objects. The topological relations between crisp spatial objects have been well identified. However how to formalise the topological relations between fuzzy regions needs more investigation. The paper starts from introduction of boundaries defined in the fuzzy topological space. By use of a definition formally equi...

The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP.