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On the Pytkeev property in spaces of continuous functions

Petr Simon·Boaz Tsaban
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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).

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Petr Simon, Boaz Tsaban. 2006-06-12. On the Pytkeev property in spaces of continuous functions. https://doi.org/10.1090/s0002-9939-07-09070-3

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