A note on the tightness of Gδ-modifications

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Abstract

We construct a normal countably tight T1 space X with t(Xδ) > 2ω. This is an answer to the question posed by Dow-Juhász-Soukup-Szentmiklóssy-Weiss [5]. We also show that if the continuum is not so large, then the tightness of Gδ-modifications of countably tight spaces can be arbitrary large up to the least ω1-strongly compact cardinal.

03E55, 54A25, 54C35

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Mar 30

Keywords

  • Countably tight
  • G-modification
  • Saturated filter
  • ω-strongly compact cardinal

ASJC Scopus subject areas

  • General

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