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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On homeomorphism groups of Menger continua


Author: Jan J. Dijkstra
Journal: Trans. Amer. Math. Soc. 357 (2005), 2665-2679
MSC (2000): Primary 57S05
Published electronically: March 1, 2005
MathSciNet review: 2139522
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Abstract: It is shown that the homeomorphism groups of the (generalized) Sierpinski carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner's proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdos space in the homeomorphism groups, is of independent interest.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03863-8
PII: S 0002-9947(05)03863-8
Keywords: Menger continuum, Sierpi\'nski carpet, homeomorphism group, topological dimension, complete Erd\H os space
Received by editor(s): July 15, 2003
Published electronically: March 1, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.