On the Pytkeev property in spaces of continuous functions
General Topology
2010-11-05 v5 Combinatorics
Logic
Abstract
Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that C_p(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natural characterization of the Pytkeev property of C_p(X) by means of a covering property of X, and to a similar result for the Reznicenko property of C_p(X).
Cite
@article{arxiv.math/0606270,
title = {On the Pytkeev property in spaces of continuous functions},
author = {Petr Simon and Boaz Tsaban},
journal= {arXiv preprint arXiv:math/0606270},
year = {2010}
}