Ascoli’s theorem for pseudocompact spaces

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

A Tychonoff space X is called (sequentially) Ascoli if every compact subset (resp. convergent sequence) of Ck(X) is equicontinuous, where Ck(X) denotes the space of all real-valued continuous functions on X endowed with the compact-open topology. The classical Ascoli theorem states that each compact space is Ascoli. We show that a pseudocompact space X is Asoli iff it is sequentially Ascoli iff it is selectively ω-bounded. The class of selectively ω-bounded spaces is studied.

Original languageEnglish
Article number174
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume114
Issue number4
DOIs
StatePublished - 1 Oct 2020

Keywords

  • Ascoli
  • C(X)
  • Compact-covering map
  • Pseudocompact
  • Selectively ω-bounded
  • Sequentially Ascoli

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Ascoli’s theorem for pseudocompact spaces'. Together they form a unique fingerprint.

Cite this