On U-equivalence spaces

TL;DR

This paper introduces and explores the concept of U-equivalence spaces, including their induced structures, open subsets, functions, and their relation to uniformisable topological spaces.

Contribution

It presents the notion of induced U-equivalence spaces and studies their properties, including open sets, functions, and their connection to uniformisable topologies.

Findings

Introduction of induced U-equivalence spaces

Characterization of U-equivalently open subsets and functions

Analysis of equivalently uniformisable topological spaces

Abstract

In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U-equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.