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.

Irreversible processes can be described in Open non-equilibrium thermodynamic systems, of topological dimension 4. By means of Continuous Topological evolution, such processes can cause local decay to Closed non-equilibrium thermodynamic states, of topological dimension 3. These topologically coherent, perhaps deformable, regions or states of one or more components appear to "emerge" as compact...

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

The notion of compatible apparition points is introduced for non-Hausdorff manifolds, and properties of these points are studied. It is well known that the Hausdorff property is independent of the other conditions given in the standard definition of a topological manifold. In much of literature, a topological manifold of dimension n is a Hausdorff topological space which has a countable base of...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...