2025/12/16 by Böhnlein, Franziska, Bruske, Benjamin, Wegner, Sven-Ake
#18A25 #18F60 #46A17 #46M15 #54B30 #54E99 #55U40 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)
paper · doi:10.48550/arxiv.2512.14612
In their 2022 lecture notes on condensed sets, Clausen and Scholze mentioned in a remark that the important subclass of quasiseparated condensed sets is equivalent to the category of so-called compactological spaces defined by Waelbroeck in the 1960s. In this paper we survey the latter category in detail, we give a rigorous proof of Clausen and Scholze's claim, and we establish that condensed sets are a formal categorical completion of Waelbroeck's compactological spaces. The latter answers a question asked by Hanson in 2023 and permits the interpretation of compactological sets as an 'elementary' approach to condensed mathematics.