on a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. in this paper we extend thisconcepts to the fuzzy case. we give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

In this paper, we present two new generalizations of the pasting lemma using soft mixed structure. To do this, introduce notions a $(\tau _{1},\tau _{2})$-$g$-closed set and _{2})$-$gpr$% -closed set. We establish $g$-soft continuity $gpr$-soft between topological spaces $(X,\tau _{1},\Delta _{1})$, _{2},\Delta _{1})$ space ,\Delta _{2})$. Finally prove versions continuous mapping mapping.

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this work, we consider the concepts of GL-soft perfect sets, GR-soft perfect sets and G -soft perfect sets were introduced in the soft topological space (X, A, τ) with a soft G which are extensions of the concepts soft τG-closed, soft τG-dense in itself and soft τG-perfect, respectively. Also, ...

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...

In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete topology using indiscernibility (equivalence) relation in rough set theory is described. Secondly, the paper describes that a “general” topology is a special case of soft set. He...