Topological Group Construction In Proximity And Descriptive Proximity Spaces

TL;DR

This paper introduces the concepts of proximal and descriptive proximal groups within proximity spaces, exploring their algebraic structures and continuity properties, thereby extending topological group theory into proximity contexts.

Contribution

It presents the novel definitions of proximal and descriptive proximal groups and analyzes their homomorphisms and isomorphisms in proximity spaces.

Findings

Defined proximal and descriptive proximal groups

Analyzed homomorphisms and isomorphisms in proximity groups

Extended topological group concepts to proximity spaces

Abstract

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the concepts of homomorphism and isomorphism, which give important results in group theory, are discussed by interpreting the concepts of continuity in the theory of (descriptive) proximity.