The natural duality between “topological” and “regular,” both considered as convergence space properties, extends naturally top-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage of this duality, the behavior ofp-topological andp-regular convergence spaces is explored, with particular emphasis on the former, since they have not been p...

A generalized fuzzy topological space called countable fuzzy topological space has already been introduced by the authors. The generalization has been performed by relaxing the criterion of preservation of arbitrary supremum of fuzzy topology to countable supremum. In this paper the notion of fuzzy compactness called c-compactness has been initiated and various properties are studied. Other rel...

The aim of this paper is to study some properties of soft Hausdorff space introduced by Shabir and Naz. Firstly, we give a representation of soft sets and soft topological spaces. Secondly, we introduce some new concepts in soft topological space such as convergence of sequences, homeomorphism and investigate the relations between these concepts and Hausdorff axiom in soft topological space. 20...

Topology is an important and major area of mathematics and it can give many relationships between other scientific areas and mathematical models.The aim of this paper is to construct intuitionistic fuzzy soft multi topological space and it is shown that an intuitionistic fuzzy soft multi topological space gives a family of parameterized topological spaces and some basic properties regarding wit...

In this paper we have introduced and studied 2α,β-connectedness and Dconnectedness in an intuitionistic fuzzy topological space as extensions of 2αconnectedness and D-connectedness respectively in a fuzzy topological space (given by Lowen and Srivastava) and proved some basic results related to it. We have also introduced some other type of connectedness in an intuitionistic fuzzy topological s...

We carefully define and study C∗-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology along the way. We explain the triangulated category structure on the bivariant Kasparov theory over a topological space and study the analogue of the bootstrap class for C∗-algebras over a finite topological space.

Topological approximation of self-formation of artificial objects in micro-scale is well established. However expansion of the topological approximation into nanoand molecular scales requires new and more generalized concepts of self-formation. This paper represents a preliminary effort to define self-formation as an evolution of 4-D parametric space in 8-D topological space, as universal conce...

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as c...

In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing perf...