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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:
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.
References:
- 1.
- Mladen Bestvina, Characterizing
-dimensional universal Menger compacta, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no.2, 369-370. MR 86g:54047 - 2.
- Mladen Bestvina, Characterizing
-dimensional universal Menger compacta, Memoirs Amer. Math. Soc 71 (1988), no. 380, vi+110 pp. MR 89g:54083 - 3.
- B. L. Brechner, On the dimensions of certain spaces of homeomorphisms, Trans. Amer. Math. Soc. 121 (1966), 516-548. MR 32:4662
- 4.
- J. E. Keesling and D. C. Wilson, An almost uniquely homogeneous subgroup of
, Topology and its Applications 22 (1986), 183-190. MR 87j:22002 - 5.
- M. Levin and R. Pol, A metric condition which implies dimension
, Proc. Amer. Math. Soc. 125 (1997), 269-273. MR 97e:54033 - 6.
- 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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