On the Pytkeev property in spaces of continuous functions
Petr Simon, Boaz Tsaban
Abstract
Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that Cp(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 Cp(X) by means of a covering property of X, and to a similar result for the Reznicenko property of Cp(X).
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