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arXiv:math/0701249 [math.GN]AbstractReferencesReviewsResources

On the Pytkeev property in spaces of continuous functions (II)

Boaz Tsaban, Lyubomyr Zdomskyy

Published 2007-01-09, updated 2010-11-04Version 6

We prove that for each Polish space X, the space C(X) of continuous real-valued functions on X satisfies a strong version of the Pytkeev property, if endowed with the compact-open topology. (This shows that whereas it need not be metrizable, it is "very close" to that.) We also consider the Pytkeev property in the case where C(X) is endowed with the topology of pointwise convergence.

Journal: Houston Journal of Mathematics, 35 (2009), 563-571
Categories: math.GN, math.FA, math.LO
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