Alonso Morón, Manuel 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.
|Uncontrolled Keywords:||Pointed shape theory; Whitehead theorem; shape morphism; Cantor completion process; invariant ultrametric; shape theory|
|Subjects:||Sciences > Mathematics > Topology|
|Deposited On:||14 Jun 2012 10:54|
|Last Modified:||14 Jun 2012 10:54|
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