Condensations of Cp(X) onto σ-compact spaces

Abstract

[EN] 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.