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Proper hereditary shape equivalences preserve small weak infinite-dimensionality

Author: Richard P. Millspaugh
Journal: Proc. Amer. Math. Soc. 110 (1990), 1055-1061
MSC: Primary 54F45; Secondary 54C10
MathSciNet review: 1037215
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Abstract: A space is said to be small weakly infinite dimensional if it has a basis $ B$ such that the collection of finite unions of elements of $ B$ is inessential. A characterization of small weak infinite dimensionality is given for locally compact spaces. This characterization is then used to prove that if $ f:X \to Y$ is a proper hereditary shape equivalence from a metric space $ X$ which is small weakly infinite dimensional onto a locally compact metric space $ Y$, then $ Y$ is small weakly infinite dimensional.

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  • [AG] D. F. Addis and J. H. Gresham, A class of infinite dimensional spaces, Part I: Dimension theory and Alexandroff's problem, Fund. Math. 101 (1978), 195-205. MR 521122 (80b:54041)
  • [A1] F. D. Ancel, Proper hereditary shape equivalences preserve property $ C$, Topology Appl. 19 (1985), 71-74. MR 786082 (86g:54026)
  • [A2] -, The role of countable dimensionality in the theory of cell-like relations, Trans. Amer. Math. Soc. 287 (1985), 1-40. MR 766204 (86b:54012)
  • [B1] P. Borst, Spaces having a weakly-infinite-dimensional compactification, Topology Appl. 21 (1985), 261-268. MR 812644 (87g:54078)
  • [B2] -, Some remarks concerning $ C$-spaces, preprint.
  • [H] S. T. Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977 (31:6202)
  • [HW] W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press, Princeton, NJ, 1941. MR 0006493 (3:312b)
  • [R] D. Rohm, Hereditary shape equivalences preserve weak infinite dimensionality, preprint.

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Keywords: Small weakly infinite dimensional, hereditary shape equivalence, approximately invertible map, inessential
Article copyright: © Copyright 1990 American Mathematical Society

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