On the Pytkeev property in spaces of continuous functions

Simon, Petr; Tsaban, Boaz

doi:10.1090/S0002-9939-07-09070-3

On the Pytkeev property in spaces of continuous functions
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by Petr Simon and Boaz Tsaban

Proc. Amer. Math. Soc. 136 (2008), 1125-1135

DOI: https://doi.org/10.1090/S0002-9939-07-09070-3

Published electronically: November 30, 2007

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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 $\mathfrak {p}$. 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 Reznichenko property of $C_p(X)$.

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