On regular but not completely regular spaces
Piotr Kalemba, Szymon Plewik
TL;DR
This paper explores the construction of regular spaces that are not completely regular, using set-theoretic frameworks and classical topological examples to generate counterexamples.
Contribution
It introduces a method to derive non-comparable regular but not completely regular spaces from set-theoretic generalizations of known examples.
Findings
Constructed new counterexamples using Niemytzki and Songefrey planes
Generalized Mysior's example through set-theoretic analysis
Demonstrated the existence of non-comparable regular but not completely regular spaces
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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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology