2024/10/23 by Dagur Tómas Ásgeirsson, Asgeirsson, Dagur
Computer Science · #Advanced Database Systems and Queries #Category Theory (math.CT) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2410.17847
openalex publication_date 2024/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can be defined as a sheaf on a certain site of compact Hausdorff spaces. Since condensed sets are supposed to be a generalization of topological spaces, one would like to be able to study the notion of discreteness. There are various ways to define what it means for a condensed set to be discrete. In this paper we describe them, and prove that they are equivalent. The results have been fully formalized in the Lean proof assistant.