Finite approximations of countable metric and ultrametric compacta

2024/12/18 by Mondéjar, Diego
Mathematics · #54B20 #54C60 #54F17 #54G15 #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Geometric Topology (math.GT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.14325

openalex publication_date 2024/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Adapting a homotopy reconstruction theorem for general metric compacta, we show that every countable metric or ultrametric compact space can be topologically reconstructed as the inverse limit of a sequence of finite T₀ spaces which are finer approximations of the space.

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