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On homeomorphism groups of Menger continua
Author(s):
Jan
J.
Dijkstra
Journal:
Trans. Amer. Math. Soc.
357
(2005),
2665-2679.
MSC (2000):
Primary 57S05
Posted:
March 1, 2005
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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:
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
Posted:
March 1, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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