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Ultrametrics and infinite dimensional whitehead theorems in shape theory

Morón, Manuel A. and Romero Ruiz del Portal, Francisco (1996) Ultrametrics and infinite dimensional whitehead theorems in shape theory. Manuscripta mathematica, 89 (1). pp. 325-333. ISSN 0025-2611

Official URL: http://www.springerlink.com/content/p682110q57204015/

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Abstract

We apply a Cantor completion process to construct a complete, non-Archimedean metric on the set of shape morphisms between pointed compacta. In the case of shape groups we obtain a canonical norm producing a complete, both left and right invariant ultrametric. On the other hand, we give a new characterization of movability and we use these spaces of shape morphisms and uniformly continuous maps between them, to prove an infinite-dimensional theorem from which we can show, in a short and elementary way, some known Whitehead type theorems in shape theory.


Item Type:Article
Uncontrolled Keywords:Pointed shape theory; Whitehead theorem; shape morphism; Cantor completion process; invariant ultrametric; shape theory
Subjects:Sciences > Mathematics > Topology
ID Code:15632
Deposited On:14 Jun 2012 08:54
Last Modified:05 Nov 2013 16:17

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