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Proceedings of the American Mathematical Society
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On the dimension of a homeomorphism group

Author(s): Beverly L. Brechner; Kazuhiro Kawamura
Journal: Proc. Amer. Math. Soc. 129 (2001), 617-620.
MSC (1991): Primary 54F45, 54G20; Secondary 54H15, 54H20
Posted: September 20, 2000
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Abstract | References | Similar articles | Additional information

Abstract:

We prove that the homeomorphism group of each one of a collection of continua constructed in a paper by the first author (Trans. Amer. Math. Soc. 121 (1966), 516-548) is one dimensional. This answers a question posed in that paper.


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B. L. Brechner, On the dimensions of certain spaces of homeomorphisms, Trans. Amer. Math. Soc. 121 (1966), 516-548. MR 32:4662

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J. E. Keesling and D. C. Wilson, An almost uniquely homogeneous subgroup of $R^n$, Topology and its Applications 22 (1986), 183-190. MR 87j:22002

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L. G. Oversteegen and E. D. Tymchatyn, On the dimension of certain totally disconnected spaces, Proc. Amer. Math. Soc. 122 (1994), 885-891. MR 95b:54040

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Additional Information:

Beverly L. Brechner
Affiliation: Department of Mathematics, University of Florida at Gainesville, Gainesville, Florida 32611-8105
Email: brechner@math.ufl.edu

Kazuhiro Kawamura
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305 Japan
Email: kawamura@math.tsukuba.ac.jp

DOI: 10.1090/S0002-9939-00-05585-4
PII: S 0002-9939(00)05585-4
Keywords: Homeomorphism group, dimension, Menger continua
Received by editor(s): June 6, 1998
Received by editor(s) in revised form: May 8, 1999
Posted: September 20, 2000
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society


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