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Analysis of a topological basis problem

Abstract

We examine a basis problem for uncountable regular first countable spaces using the Proper Forcing Axiom. We introduce a notion of inner and outer topologies and show that they come quite close to characterizing the correctness of the current conjecture about this basis problem.

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Correspondence to Y. Peng.

Additional information

The research of the second author was partially supported by grants from NSERC (455916) and CNRS (UMR7586).

Peng was partially supported by NSFC No. 11901562 and a program of the Chinese Academy of Sciences.

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Peng, Y., Todorcevic, S. Analysis of a topological basis problem. Acta Math. Hungar. 167, 419–475 (2022). https://doi.org/10.1007/s10474-022-01253-y

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  • DOI: https://doi.org/10.1007/s10474-022-01253-y

Key words and phrases

  • basis problem
  • countable network
  • Sorgenfrey space

Mathematics Subject Classification

  • 54A35
  • 54D20
  • 03E75