In this paper, a new class of generalized separation axioms (briefly, g-Tg-separation axioms) whose elements are called g-Tg,K, g-Tg,F, g-Tg,H, g-Tg,R, g-Tg,N-axioms is defined in terms sets g-Tg-sets) topological spaces Tg-spaces) and the properties characterizations Tg-space endowed with each such discussed. The study shows that g-Tg,F-axiom implies g-Tg,K-axiom, g-Tg,H-axiom g-Tg,F-axiom, g-...

We use Chen iterated line integrals to construct a topological algebra Ap of separating functions on the Group of Loops LMp. Ap has an Hopf algebra structure which allows the construction of a group structure on its spectrum. We call this topological group, the group of generalized loops L̃Mp. Then we develope a Loop Calculus, based on the Endpoint and Area Derivative Operators, providing a rigo...

Given a sequence of Galerkin spaces Xh of curl conforming vector fields, we state necessary and sufficient conditions under which it is true that the scalar product uh ·uh of two sequences of vector fields uh, uh ∈ Xh converging weakly in L, converges in the sense of distributions to the right limit, whenever uh is discrete divergence free and curluh is precompact in H−1. The conditions on Xh a...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

The main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (briefly soft rgb-closed set) Moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g$alpha$-closed, soft g$alpha$b-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and w...

In this paper we introduce a notion of dimension and codimension for every element of a distributive bounded lattice L. These notions prove to have a good behavior when L is a co-Heyting algebra. In this case the codimension gives rise to a pseudometric on L which satisfies the ultrametric triangle inequality. We prove that the Hausdorff completion of L with respect to this pseudometric is prec...

The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical pro...

In the problem of classical group testing one aims to identify a small subset (of size $d$ ) diseased individuals/defective items in large population notation="LaTeX">$n$ ). This process is based on minimal number suitably-designed te...

In this paper, we first generalize a fixed point theorem due to Tarafdar from topological vector spaces to general topological spaces without linear structure. By using our new fixed point theorem, some new existence theorems of solutions for generalized vector equilibrium problems and generalized implicit vector variational inequality problems are proved under noncompact settings of general to...