The space of all selfhomeomorphisms of a twocell which fix the cell's boundary is an absolute retract
Author:
W. K. Mason
Journal:
Trans. Amer. Math. Soc. 161 (1971), 185205
MSC:
Primary 54.28
MathSciNet review:
0286067
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References 
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Additional Information
Abstract: The theorem mentioned in the title is proved. A corollary of the title theorem is: any homeomorphism between two compact subsets of the function space mentioned in the title can be extended to a homeomorphism of the function space onto itself.
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 J. W. Alexander, On the deformation of an ncell, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 406407.
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 [3]
 , Spaces of homeomorphisms of finite graphs (to appear).
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 R. D. Anderson and R. H. Bing, A complete elementary proof that hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 74 (1968), 771792. MR 37 #5847. MR 0230284 (37:5847)
 [5]
 M. Brown, Pushing graphs around, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967), Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 1922. MR 38 #2785. MR 0234468 (38:2785)
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 K. Borsuk, Über eine Klasse von lokal zusammenhangenden Räumen, Fund. Math. 19 (1932), 220240.
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 C. H. Dowker, Mapping theorems for noncompact spaces, Amer. J. Math. 69 (1947), 200242. MR 8, 594. MR 0020771 (8:594g)
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 E. Dyer and M.E. Hamstrom, Regular mappings and the space of homeomorphisms on a 2manifold, Duke Math. J. 25 (1958), 521531. MR 20 #2695. MR 0096202 (20:2695)
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 M.E. Hamstrom, Regular mappings and the space of homeomorphisms on a 3manifold, Mem. Amer. Math. Soc. No. 40 (1961). MR 27 #2970. MR 0152999 (27:2970)
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 , Some global properties of the space of homeomorphisms of a disc with holes, Duke Math. J. 29 (1962), 657662. MR 26 #745. MR 0143185 (26:745)
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 G. Simmons, Introduction to topology and modern analysis, McGrawHill, New York, 1963. MR 26 #4145. MR 0146625 (26:4145)
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 A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977982. MR 10, 204. MR 0026802 (10:204c)
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 Problems on infinitedimensional spaces and manifolds, Louisiana State University, Baton Rouge, La., 1969 (mimeographed).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197102860679
PII:
S 00029947(1971)02860679
Keywords:
Retract,
absolute retract,
twocell,
twomanifold,
twomanifold function space,
space of homeomorphisms,
infinitedimensional manifold
Article copyright:
© Copyright 1971
American Mathematical Society
