In this paper the concept of metacompactness in L-topologicalspaces is introduced by means of point finite families of L-fuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedL-topological spaces is also obtained.

Finite SLH topological spaces are characterized as partition topological spaces. As a consequence, two partial answers for a question raised in [3] are obtained. Closed-homogeneous topological spaces are characterized. Having a minimal open set is proved to be a sufficient condition for a homogeneous topological space to be closed-homogeneous. Closed-homogeneity is extended to include fuzzy top...

Algebraic topology consists in associating to topological spaces algebraic invariants in order to describe their essential properties. In some (exceptional) cases, it is possible in this way to classify a particular topological space inside a more or less large set of spaces or equivalence classes of spaces, for example up to homotopy equivalence. In the most important cases, a functor is defin...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

In this paper, we aim to develop a suitable homotopy theory of finite topological graphs by Khalimsky arcs. The notions developed are considered for the investigation of the algebraic invariants of topological graphs for their topological and graphical classifications. Keywords—Connected ordered topological spaces, digital topology, homotopy, Khalimsky spaces, topological graphs.

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...