There are no uniquely homogeneous spaces
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- by William Barit and Peter Renaud PDF
- Proc. Amer. Math. Soc. 68 (1978), 385-386 Request permission
Abstract:
One could say a continuum is uniquely homogeneous if for each pair of points there is a unique homeomorphism taking the one point to the other. Ungar showed that such spaces are topological groups with no automorphisms. This note shows there are no such nontrivial groups.References
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E. Burgess, Homogenous continua, Summary of Lectures and Seminars, Summer Institute on Set Theoretic Topology, University of Wisconsin, 1955, pp. 75-78.
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
- Gerald S. Ungar, On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393–400. MR 385825, DOI 10.1090/S0002-9947-1975-0385825-3
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 385-386
- MSC: Primary 54F20; Secondary 22D45, 22D05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0464187-5
- MathSciNet review: 0464187