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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Pytkeev property in spaces of continuous functions


Authors: Petr Simon and Boaz Tsaban
Journal: Proc. Amer. Math. Soc. 136 (2008), 1125-1135
MSC (2000): Primary 54C35, 03E17
Published electronically: November 30, 2007
MathSciNet review: 2361889
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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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Additional Information

Petr Simon
Affiliation: Department of Computer Science and Mathematical Logic, Charles University, Malostranské nám. 25, 11000 Praha 1, Czech Republic.
Email: psimon@ms.mff.cuni.cz

Boaz Tsaban
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel; and Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Email: tsaban@math.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09070-3
PII: S 0002-9939(07)09070-3
Received by editor(s): June 20, 2006
Received by editor(s) in revised form: November 16, 2006
Published electronically: November 30, 2007
Additional Notes: The second author was partially supported by the Koshland Center for Basic Research.
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society