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

 

A counterexample concerning line-free groups and complete Erdos space


Authors: Jan J. Dijkstra and Jan van Mill
Journal: Proc. Amer. Math. Soc. 134 (2006), 2281-2283
MSC (2000): Primary 46B25, 54F45
Published electronically: February 2, 2006
MathSciNet review: 2213700
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Abstract: We present a weakly closed, one-dimensional, line-free subgroup of the separable Banach space $ c$ that is not homeomorphic to complete Erdos space. The existence of this example disproves a conjecture of Dobrowolski, Grabowski, and Kawamura.


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Additional Information

Jan J. Dijkstra
Affiliation: Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081$^{a}$, 1081 HV Amsterdam, The Netherlands
Email: dijkstra@cs.vu.nl

Jan van Mill
Affiliation: Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081$^{a}$, 1081 HV Amsterdam, The Netherlands
Email: vanmill@cs.vu.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08232-3
PII: S 0002-9939(06)08232-3
Keywords: Banach space, line-free group, weakly closed, complete Erd\H os space, almost zero-dimensional
Received by editor(s): December 8, 2004
Received by editor(s) in revised form: February 25, 2005
Published electronically: February 2, 2006
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.