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.

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

There are two main approaches to obtaining \topological" cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed | for example, the category of sequential spaces. Under the other, one generalises the notion of space | for example, to Scott's notion of equilogical space. In this paper we show that the two appr...

in this paper, some fundamental concepts are given relating to fuzzytopological spaces. then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. also the fuzzy topological spaces which are hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...