On extending homeomorphisms to Fréchet manifolds
Authors:
R. D. Anderson and John D. McCharen
Journal:
Proc. Amer. Math. Soc. 25 (1970), 283289
MSC:
Primary 57.55
MathSciNet review:
0258064
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Abstract: Let be a Fréchet manifold and be a set in . It is shown that a homeomorphism of into can be isotopically extended to a homeomorphism of onto if and only if is a set and is homotopic to the identity in . Conditions under which the isotopic extension can be required to be ``close to'' the homotopy are also given.
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D. Anderson and R.
Schori, A factor theorem for Fréchet
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 [1]
 R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515519. MR 32 #8298. MR 0190888 (32:8298)
 [2]
 , Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200216. MR 34 #5045. MR 0205212 (34:5045)
 [3]
 , On topological infinite deficiency, Michigan Math. J. 14 (1967), 365383. MR 35 #4893. MR 0214041 (35:4893)
 [4]
 R. D. Anderson, David W. Henderson, and James E. West, Negligible subsets of infinitedimensional manifolds, Compositio Math. 21 (1969), 143150. MR 0246326 (39:7630)
 [5]
 R. D. Anderson and R. M. Schori, A factor theorem for Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 5356. MR 38 #1704. MR 0233382 (38:1704)
 [6]
 T. A. Chapman, Infinite deficiency in Fréchet manifolds, Trans. Amer. Math. Soc. 148 (1970), 568573. MR 0256418 (41:1074)
 [7]
 David W. Henderson, Infinitedimensional manifolds are open subsets of Hilbert space, Bull. Amer. Math. Soc. 75 (1969), 759762. MR 0247634 (40:898)
 [8]
 V. L. Klee, Jr., Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 3045. MR 16, 1030. MR 0069388 (16:1030c)
 [9]
 James E. West, Approximating homotopies by isotopies in Fréchet manifolds. Bull. Amer. Math. Soc. 75 (1969), 12541257. MR 0248792 (40:2042)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197002580645
PII:
S 00029939(1970)02580645
Keywords:
Fréchet manifolds,
infinitedimensional manifolds,
sets,
Property ,
homeomorphism extension,
ambient isotopy
Article copyright:
© Copyright 1970
American Mathematical Society
