A metric space with the Haver property whose square fails this property
Authors:
Elzbieta Pol and Roman Pol
Journal:
Proc. Amer. Math. Soc. 137 (2009), 745750
MSC (2000):
Primary 54D20, 54F45, 54E50
Published electronically:
August 25, 2008
MathSciNet review:
2448597
Fulltext PDF
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Abstract: Haver introduced the following property of metric spaces : for each sequence of positive numbers there exist collections of open subsets of , the union of which covers , such that the members of are pairwise disjoint and every member of has diameter less than . We construct two separable complete metric spaces , with the Haver property such that , generate the same topology on , but fails this property. In particular, the square of a separable complete metric space with the Haver property may fail this property. Our results answer some questions posed by Babinkostova in 2007.
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Additional Information
Elzbieta Pol
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02097 Warszawa, Poland
Email:
pol@mimuw.edu.pl
Roman Pol
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02097 Warszawa, Poland
Email:
pol@mimuw.edu.pl
DOI:
http://dx.doi.org/10.1090/S0002993908095117
PII:
S 00029939(08)095117
Keywords:
Haver property,
property $C$,
product spaces.
Received by editor(s):
September 24, 2007
Received by editor(s) in revised form:
January 25, 2008
Published electronically:
August 25, 2008
Additional Notes:
The first author was partially supported by MNiSW Grant No. N201 034 31/2717
Communicated by:
Alexander N. Dranishnikov
Article copyright:
© Copyright 2008 American Mathematical Society
