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2002 Metrizable shape and strong shape equivalences
L. Stramaccia
Homology Homotopy Appl. 4(1): 71-85 (2002).

Abstract

In this paper we construct a functor $\Phi : \rm{pro}\mathcal{T}op \to \rm{pro}\mathcal{ANR}$ which extends Mardešic correspondence that assigns to every metrizable space its canonical $\mathcal{ANR}$-resolution. Such a functor allows one to define the strong shape category of prospaces and, moreover, to define a class of spaces, called strongly fibered, that play for strong shape equivalences the role that $\mathcal{ANR}$-spaces play for ordinary shape equivalences. In the last section we characterize SSDR-promaps, as defined by Dydak and Nowak, in terms of the strong homotopy extension property considered by the author.

Citation

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L. Stramaccia. "Metrizable shape and strong shape equivalences." Homology Homotopy Appl. 4 (1) 71 - 85, 2002.

Information

Published: 2002
First available in Project Euclid: 13 February 2006

zbMATH: 1030.18009
MathSciNet: MR1937959

Subjects:
Primary: 54C56
Secondary: 54B30 , 55P55 , 55P65

Rights: Copyright © 2002 International Press of Boston

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Vol.4 • No. 1 • 2002
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