Year: 2024
Type: preprint
Abstract: In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete spaces. This subcategory is closely related to a particular subcategory of locales, offering an alternative approach to localic completion. Additionally, we demonstrate how this framework provides simple constructive definitions of compact spaces, uniform convergence, and limits of nets.
Source: arXiv (Cornell University)
Author: Isaev, Valery
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405957147