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.

Original languageEnglish
Article number106820
JournalTopology and its Applications
Volume265
DOIs
Publication statusPublished - 2019 Sep 15

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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