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

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

2007-01-09

arxiv.org/abs/math/0701249v6

Houston Journal of Mathematics, 35 (2009), 563-571

Mathematics

General Topology

Scientific paper

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.

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