A classification of the cofinal structures of precompacta

Aviv Eshed, M. Vicenta Ferrer, Salvador Hernández, Piotr Szewczak, Boaz Tsaban

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Abstract

We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we classify the cofinal structure of local bases in the groups C(X,R) of continuous real-valued functions on complete metric spaces X, with respect to the compact-open topology.

Original languageEnglish
Article number102810
JournalAnnals of Pure and Applied Logic
Volume171
Issue number8
DOIs
StatePublished - 1 Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Compact sets
  • Compact-open topology
  • Local density
  • Precompact sets
  • Tukey equivalence

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