Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On homeomorphisms of infinite dimensional bundles. II

Authors: T. A. Chapman and R. Y. T. Wong
Journal: Trans. Amer. Math. Soc. 191 (1974), 261-268
MSC: Primary 57A20; Secondary 58B05
MathSciNet review: 0415626
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper presents some aspects of homeomorphism theory in the setting of (fibre) bundles modeled on separable Hilbert manifolds and generalizes results previously established. The main result gives a characterization of subsets of infinite deficiency in a bundle by means of their restriction to the fibres, from which we are able to prove theorems of the following types: (a) mapping replacement, (b) separation of sets, (c) negligibility of subsets, and (d) extending homeomorphisms.

References [Enhancements On Off] (What's this?)

  • [1] 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), 771-792. MR 37 #5847. MR 0230284 (37:5847)
  • [2] R. D. Anderson, D. Henderson and J. West, Negligible subsets of infinite-dimensional manifolds, Compositio Math. 21 (1969), 143-150. MR 39 #7630. MR 0246326 (39:7630)
  • [3] R. D. Anderson and J. D. MeCharen, On extending homeomorphisms to Fréchet manifolds, Proc. Amer. Math. Soc. 25 (1970), 283-289. MR 41 #2711. MR 0258064 (41:2711)
  • [4] R. D. Anderson and R. Schori, Factors of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 142 (1969), 315-330. MR 39 #7631. MR 0246327 (39:7631)
  • [5] T. A. Chapman, Infinite deficiency in Fréchet manifolds, Trans. Amer. Math. Soc. 148 (1970), 137-146. MR 41 #1074. MR 0256418 (41:1074)
  • [6] D. W. Henderson, Infinite-dimensional manifolds are open subsets of Hilbert space, Bull. Amer. Math. Soc. 75 (1969), 759-762. MR 40 #898. MR 0247634 (40:898)
  • [7] R. Y. T. Wong, On homeomorphisms of infinite-dimensional bundles. I, Trans. Amer Math. Soc. 191 (1974, 245-259. MR 0415625 (54:3708a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57A20, 58B05

Retrieve articles in all journals with MSC: 57A20, 58B05

Additional Information

Keywords: Bundle, polyhedron, homeomorphism, ambient isotopy
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society