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 | References | Similar Articles | Additional Information

Abstract: Answering a question of Sakai, we show that the minimal cardinality of a set of reals such that does not have the Pytkeev property is equal to the pseudo-intersection number . Our approach leads to a natural characterization of the Pytkeev property of by means of a covering property of , and to a similar result for the Reznichenko property of .

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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

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