Homeomorphism groups of some direct limit spaces
Author:
Margie Hale
Journal:
Proc. Amer. Math. Soc. 85 (1982), 661665
MSC:
Primary 57S05; Secondary 54H15, 57N20, 58B05
MathSciNet review:
660625
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Let be either of the spaces or where denotes the reals and the Hilbert cube. Let be the homeomorphism group of a connected manifold with the compactopen topology. We prove that is separable, Lindelöf, paracompact, nonfirstcountable, and not a space.
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 R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515519. MR 0190888 (32:8298)
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 James Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 0193606 (33:1824)
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 Steve Ferry, The homeomorphism group of a compact Hilbert cube manifold is an ANR, Ann. of Math. (2) 106 (1977), 101119. MR 0461536 (57:1521)
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 Margie Hale, A factoring technique for homeomorphism groups (to appear). MR 672461 (83k:57009)
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 V. L. Hansen, Some theorems on direct limits of expanding sequences of manifolds, Math. Scand. 29 (1971), 536. MR 0319206 (47:7751)
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 R. E. Heisey, Contracting spaces of maps on the countable direct limit of a space, Trans. Amer. Math. Soc. 193 (1974), 389411. MR 0367908 (51:4150)
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 , Manifolds modeled on or bounded weak* topologies, Trans. Amer. Math. Soc. 206 (1975), 295312. MR 0397768 (53:1626)
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 , Manifolds modeled on the direct limit of Hilbert cubes, Proc. Conf. Geometric Topology, Univ. of Georgia, 1977.
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 , Stability, classification, open embeddings, and triangulation of manifolds, Proc. Internat. Conf. Geometric Topology, Polish Scientific Publishers, Warsaw, 1980, pp. 193196.
 [10]
 VoThanh Liem, An approximation theorem for manifolds, Topology Appl. 12 (1981), 289304. MR 623737 (82k:57011)
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 , An unknotting theorem in manifolds, Proc. Amer. Math. Soc. 82 (1981), 125132. MR 603615 (82j:57012)
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 , An approximation theorem for manifolds, preprint.
 [13]
 Peter L. Renz, The contractibility of the homeomorphism group of some product spaces by Wong's method, Math. Scand. 28 (1971), 182188. MR 0305426 (46:4556)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206606254
PII:
S 00029939(1982)06606254
Keywords:
Homeomorphism group,
direct limit,
compactopen topology,
manifold
Article copyright:
© Copyright 1982
American Mathematical Society
