Condensations of Cp(X) onto σ-compact spaces

• Tkachuk, Vladimir V. ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 1, 2009, págs. 39-48
• Idioma: inglés
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• Resumen

  • We show, in particular, that if nw(Nt) ≤  k for any t ϵ  T and C is a dense subspace of the product ǁ{Nt : t 2 T} then, for any continuous (not necessarily surjective) map ϕ : C ͢  K of C into a compact space K with t(K) ≤ k, we have ψ(ϕ (C)) ≤ k. This result has several applications in Cp-theory. We prove, among other things, that if K is a non-metrizable Corson compact space then Cp(K) cannot be condensed onto a σ-compact space. This answers two questions published by Arhangel’skii and Pavlov.