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), 745-750

MSC (2000):
Primary 54D20, 54F45, 54E50

DOI:
https://doi.org/10.1090/S0002-9939-08-09511-7

Published electronically:
August 25, 2008

MathSciNet review:
2448597

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Abstract | References | Similar Articles | Additional Information

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, 02-097 Warszawa, Poland

Email:
pol@mimuw.edu.pl

**Roman Pol**

Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Email:
pol@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-08-09511-7

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