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On regular but not completely regular spaces

2017/01/16 by Piotr Kalemba, Kalemba, Piotr, Szymon Plewik +1
Mathematics · #54D10 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.GN #msc:54D10

paper · pdf · doi:10.48550/arxiv.1701.04322

arxiv created 2017/01/16 · openalex publication_date 2017/01/16 · arxiv updated 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present how to obtain non-comparable regular but not completely regular spaces. We analyze a generalization of Mysior's example, extracting its underlying purely set-theoretic framework. This enables us to build simple counterexamples, using the Niemytzki plane, the Songefrey plane or Lusin gaps.

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