Ascoli’s theorem for pseudocompact spaces

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6 Scopus citations


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
Issue number4
StatePublished - 1 Oct 2020


  • 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


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