On the pytkeev property in spaces of continuous functions

Petr Simon; Boaz Tsaban

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

On the pytkeev property in spaces of continuous functions

Petr Simon, Boaz Tsaban

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 Reznichenko property of C_p(X).

Original language	English
Pages (from-to)	1125-1135
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-07-09070-3
State	Published - Mar 2008

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On the pytkeev property in spaces of continuous functions

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