Existence of well-filterifications of T₀ topological spaces

2019/06/26 by Guohua Wu, Wu, Guohua, Xiaoyong Xi +5
Mathematics · #06B30 #06B35 #54A05 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1906.10832

openalex publication_date 2019/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for every T₀ space X, there is a well-filtered space W(X) and a continuous mapping η_X: X\lra W(X) such that for any well-filtered space Y and any continuous mapping f: X\lra Y there is a unique continuous mapping f: W(X)\lra Y such that f=f∘ η_X. Such a space W(X) will be called the well-filterification of X. This result gives a positive answer to one of the major open problems on well-filtered spaces. Another result on well-filtered spaces we will prove is that the product of two well-filtered spaces is well-filtered.

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