On strongly paracompact and uniformly paracompact locales

Abstract

This study investigates the properties of strongly paracompact and uniformly paracompact spaces into locales. The research builds on the work of Rice [31], Frolik [15], and Borubaev [3], who expanded the concept of paracompact spaces, making it applicable to a wider range of topological situations and allowing for the use of more ideas. The main interest lies in exploring the strongly uniformly paracompact property. The dissertation looks into how recently introduced paracompactness concepts such as R paracompactness Rice [31], can be adapted into locales. In the context of a uniform space (X, U), the study defines a space as uniformly R-paracompact if every open covering has an open, uniformly locally finite refinement.. The research aims to provide a thorough exploration of these concepts, contributing to a deeper understanding of their implications within the context of uniform spaces.