Topological properties of function spaces over ordinals

Saak Gabriyelyan, Jan Grebík, Jerzy Ka̧kol, Lyubomyr Zdomskyy

Research output: Contribution to journalArticlepeer-review


A topological space X is said to be an Ascoli space if any compact subset K of Ck(Y) is evenly continuous. This definition is motivated by the classical Ascoli theorem. We study the kR-property and the Ascoli property of Cp(κ) and Ck(κ) over ordinals κ. We prove that Cp(κ) is always an Ascoli space, while Cp(κ) is a kR-space iff the cofinality of κ is countable. In particular, this provides the first Cp-example of an Ascoli space which is not a kR-space, namely Cp1). We show that Ck(κ) is Ascoli iff cf (κ) is countable iff Ck(κ) is metrizable.

Original languageAmerican English
Pages (from-to)1157-1161
Number of pages5
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Issue number4
StatePublished - 1 Oct 2017


  • Ascoli
  • C(X)
  • C(X)
  • Ordinal space
  • k-space

All Science Journal Classification (ASJC) codes

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


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