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A Constructive Approach to Complete Spaces

2024/12/30 by Isaev, Valery
Engineering · #Architecture and Computational Design #Urban Design and Spatial Analysis

paper · pdf · doi:10.48550/arxiv.2412.20835

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.

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