Distinguished Cp(X) spaces

J. C. Ferrando, J. Ka̧kol, A. Leiderman, S. A. Saxon

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We continue our initial study of Cp(X) spaces that are distinguished, equiv., are large subspaces of RX, equiv., whose strong duals Lβ(X) carry the strongest locally convex topology. Many are distinguished, many are not. All Lβ(X) spaces are, as are all metrizable Cp(X) and Ck(X) spaces. To prove a space Cp(X) is not distinguished, we typically compare the character of Lβ(X) with |X|. A certain covering for X we call a scant cover is used to find distinguished Cp(X) spaces. Two of the main results are: (i) Cp(X) is distinguished if and only if its bidual E coincides with RX, and (ii) for a Corson compact space X, the space Cp(X) is distinguished if and only if X is scattered and Eberlein compact.

Original languageEnglish
Article number27
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume115
Issue number1
DOIs
StatePublished - 1 Jan 2021

Keywords

  • Bidual space
  • Distinguished space
  • Eberlein compact space
  • Fréchet space
  • Fundamental family of bounded sets
  • G-dense subspace
  • Point-finite family
  • strongly splittable space

ASJC Scopus subject areas

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

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