Free actions of zero-dimensional compact groups on Menger manifolds
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- by Katsuro Sakai PDF
- Proc. Amer. Math. Soc. 122 (1994), 647-648 Request permission
Abstract:
It is proved that every separable zero-dimensional compact group acts freely on any Menger manifold M. In case M is compact, this result was proved by Dranishnikov. Here is provided an alternative short proof.References
- 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
- A. N. Dranishnikov, Free actions of $0$-dimensional compact groups, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), no. 1, 212–228 (Russian); English transl., Math. USSR-Izv. 32 (1989), no. 1, 217–232. MR 936531, DOI 10.1070/IM1989v032n01ABEH000755
- Dennis J. Garity, James P. Henderson, and David G. Wright, Menger spaces and inverse limits, Pacific J. Math. 131 (1988), no. 2, 249–259. MR 922217
- L. S. Pontryagin, Nepreryvnye gruppy, 4th ed., “Nauka”, Moscow, 1984 (Russian). MR 767087
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 647-648
- MSC: Primary 57S10; Secondary 22C05, 54F15, 54H15
- DOI: https://doi.org/10.1090/S0002-9939-1994-1249889-4
- MathSciNet review: 1249889