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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/

## 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 |
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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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