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Function spaces and d-separability


VV Tkachuk

Abstract

The object of this paper is to study when a function space is d-separable, i.e., has a dense σ-discrete subspace. Several sufficient conditions are obtained for Cp(X) to be d-separable; as an application it is proved that Cp(X) is d-separable for any Corson compact space X. We give a characterization for Cp(X) × Cp(X) to be d-separable and construct, under CH, an example of a non-d-separable space X such that X × X is d-separable. We also establish that if X is a Gul’fko space (i.e., Cp(X) is LindelöNof ∑) then any subspace of X is d-separable.
Keywords: Lindelöf ∑-space, Gul'ko space, d-separable space, condensation, i-weight

Quaestiones Mathematicae 28(2005), 409–424.

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eISSN: 1727-933X
print ISSN: 1607-3606