Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Discrete cells properties in the boundary set setting

Author: Philip L. Bowers
Journal: Proc. Amer. Math. Soc. 93 (1985), 735-740
MSC: Primary 57N20
MathSciNet review: 776212
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be the complement of a $ \sigma - Z$-set in a locally compact separable ANR. It is proved that $ X$ satisfies the discrete $ n$-cells property for each nonnegative integer $ n$ if and only if $ X$ satisfies the discrete approximation property. As a consequence, Hilbert space manifolds that arise as complements of boundary sets in Hilbert cube manifolds are characterized in terms of their homological structure coupled with a minimal amount of general positioning.

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

  • [BBMW] M. Bestvina, P. Bowers, J. Mogilski and J. Walsh, Characterization of Hilbert space manifolds revisited, preprint. MR 872478 (88k:57024)
  • [Bol] P. L. Bowers, Applications of general position properties of dendrites to Hilbert space topology, Ph.D. Diss., Univ. of Tennessee, 1983.
  • [Bo2] -, Dense embeddings of sigma-compact, nowhere locally compact metric spaces, preprint.
  • [Cu] D. W. Curtis, Boundary sets in the Hilbert cube, Topology and Appl. (to appear). MR 804034 (87d:57014)
  • [DW] R. J. Daverman and J. J. Walsh, Čech homology characterizations of infinite dimensional manifolds, Amer. J. Math. 103 (1981), 411-435. MR 618319 (83k:57008)
  • [To1] H. Torunczyk, On CE-images of the Hilbert cube and characterization of $ Q$-manifolds, Fund. Math. 106 (1980), 31-40. MR 585543 (83g:57006)
  • [To2] -, Characterizing Hilbert space topology, Fund. Math 111 (1981), 247-262. MR 611763 (82i:57016)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N20

Retrieve articles in all journals with MSC: 57N20

Additional Information

Keywords: Discrete approximation property, discrete $ n$-cells property
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society