Ultrametrics and infinite dimensional whitehead theorems in shape theory



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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/


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:12 Dec 2018 15:13

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