English

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

General Topology 2010-11-05 v6 Functional Analysis Logic

Abstract

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.

Keywords

Cite

@article{arxiv.math/0701249,
  title  = {On the Pytkeev property in spaces of continuous functions (II)},
  author = {Boaz Tsaban and Lyubomyr Zdomskyy},
  journal= {arXiv preprint arXiv:math/0701249},
  year   = {2010}
}
R2 v1 2026-07-22T17:49:05.417Z