Uniqueness results for homeomorphism groups
HTML articles powered by AMS MathViewer
- by Robert R. Kallman PDF
- Trans. Amer. Math. Soc. 295 (1986), 389-396 Request permission
Abstract:
Let $X$ be a separable metric manifold and let $\mathcal {H}(X)$ be the homeomorphism group of $X$. Then $\mathcal {H}(X)$ has a unique topology in which it is a complete separable metric group. Similar results are demonstrated for a much wider class of spaces, $X$, and for many subgroups of the homeomorphism group.References
- R. D. Anderson, The algebraic simplicity of certain groups of homeomorphisms, Amer. J. Math. 80 (1958), 955–963. MR 98145, DOI 10.2307/2372842 S. Banach. Théorie des opérations linéaires, PWN, Warsaw, 1932.
- P. Chernoff and J. Marsden, On continuity and smoothness of group actions, Bull. Amer. Math. Soc. 76 (1970), 1044–1049. MR 265510, DOI 10.1090/S0002-9904-1970-12552-6
- R. P. Filipkiewicz, Isomorphisms between diffeomorphism groups, Ergodic Theory Dynam. Systems 2 (1982), no. 2, 159–171 (1983). MR 693972, DOI 10.1017/s0143385700001486
- Andrew M. Gleason and Richard S. Palais, On a class of transformation groups, Amer. J. Math. 79 (1957), 631–648. MR 89367, DOI 10.2307/2372567
- Robert R. Kallman, A uniqueness result for the infinite symmetric group, Studies in analysis, Adv. in Math. Suppl. Stud., vol. 4, Academic Press, New York-London, 1979, pp. 321–322. MR 546814
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- George W. Mackey, Borel structure in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134–165. MR 89999, DOI 10.1090/S0002-9947-1957-0089999-2
- R. Daniel Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, Mass., 1981. Mathematics from the Scottish Café; Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. MR 666400
- Jacob Palis Jr. and Welington de Melo, Geometric theory of dynamical systems, Springer-Verlag, New York-Berlin, 1982. An introduction; Translated from the Portuguese by A. K. Manning. MR 669541
- James V. Whittaker, On isomorphic groups and homeomorphic spaces, Ann. of Math. (2) 78 (1963), 74–91. MR 150750, DOI 10.2307/1970503
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 295 (1986), 389-396
- MSC: Primary 57S05; Secondary 22A05, 54H05, 54H15, 58D05
- DOI: https://doi.org/10.1090/S0002-9947-1986-0831205-0
- MathSciNet review: 831205