On the dimension of a homeomorphism group

Brechner, Beverly; Kawamura, Kazuhiro

doi:10.1090/S0002-9939-00-05585-4

On the dimension of a homeomorphism group
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by Beverly L. Brechner and Kazuhiro Kawamura PDF

Proc. Amer. Math. Soc. 129 (2001), 617-620 Request permission

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

Mladen Bestvina, Characterizing $k$-dimensional universal Menger compacta, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 369–370. MR 752801, DOI 10.1090/S0273-0979-1984-15313-8
Mladen Bestvina, Characterizing $k$-dimensional universal Menger compacta, Mem. Amer. Math. Soc. 71 (1988), no. 380, vi+110. MR 920964, DOI 10.1090/memo/0380
Beverly L. Brechner, On the dimensions of certain spaces of homeomorphisms, Trans. Amer. Math. Soc. 121 (1966), 516–548. MR 187208, DOI 10.1090/S0002-9947-1966-0187208-2
James E. Keesling and David C. Wilson, An almost uniquely homogeneous subgroup of $\textbf {R}^n$, Topology Appl. 22 (1986), no. 2, 183–190. MR 836325, DOI 10.1016/0166-8641(86)90008-8
Michael Levin and Roman Pol, A metric condition which implies dimension $\leq 1$, Proc. Amer. Math. Soc. 125 (1997), no. 1, 269–273. MR 1389528, DOI 10.1090/S0002-9939-97-03856-2
Lex G. Oversteegen and E. D. Tymchatyn, On the dimension of certain totally disconnected spaces, Proc. Amer. Math. Soc. 122 (1994), no. 3, 885–891. MR 1273515, DOI 10.1090/S0002-9939-1994-1273515-1