The Cp-stable closure of the class of separable metrizable spaces

Taras Banakh, Saak Gabriyelyan

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Denote by Cp[M0] the Cp-stable closure of the class M0 of all separable metrizable spaces, i.e., Cp[M0] is the smallest class of topological spaces that contains M0 and is closed under taking subspaces, homeomorphic images, countable topological sums, countable Tychonoff products, and function spaces Cp(X, Y). Using a recent deep result of Chernikov and Shelah, we prove that Cp[M0] coincides with the class of all Tychonoff spaces of cardinality strictly less than ℶω1. Being motivated by the theory of generalized metric spaces, we also characterize other natural Cp-type stable closures of M0.

Original languageEnglish
Pages (from-to)283-294
Number of pages12
JournalColloquium Mathematicum
Issue number2
StatePublished - 1 Jan 2017


  • Countable network
  • Function space
  • Ordered field
  • Separately continuous function
  • Topology of pointwise convergence

ASJC Scopus subject areas

  • Mathematics (all)


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