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On the Pytkeev property in spaces of continuous functions
Author(s):
Petr
Simon;
Boaz
Tsaban
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1125-1135.
MSC (2000):
Primary 54C35, 03E17
Posted:
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  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  .
References:
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- 1.
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- 2.
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- M. Sakai, The Pytkeev property and the Reznichenko property in function spaces, Note di Matematica 22 (2003), 43-52. MR 2112730 (2005i:54020)
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- 8.
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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:
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
Posted:
November 30, 2007
Additional Notes:
The second author was partially supported by the Koshland Center for Basic Research.
Communicated by:
Julia Knight
Copyright of article:
Copyright
2007,
American Mathematical Society
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