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Ultrametric spaces, valued and semivalued groups arising from the theory of shape

Cuchillo Ibáñez, Eduardo and Morón, Manuel A. and Romero Ruiz del Portal, Francisco (2012) Ultrametric spaces, valued and semivalued groups arising from the theory of shape. In Contribuciones matemáticas en honor a Juan Tarrés. UCM, Madrid, pp. 81-92. ISBN 978-84-695-4421-1

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Abstract

In this paper we construct many generalizad ultrametrics in the sets of shape morphisms between topological spaes. We recognize a topology in these sets which is independen on the shape representation of the spaces. We construct valuations an semivaluations on groups of shape equivalences and on n-th shape groups. We also connect shape theory, for arbitrary topological spaces, with the algebraic theory of generalized ultrametric spaces developed by S. Priess-Crampe and P. Ribenboim among other authors.

Item Type:Book Section
Uncontrolled Keywords:Shape morphisms; shape equivalences; shape groups; ultrametrics; valuations and semivaluations on groups
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17352
Deposited On:10 Dec 2012 09:41
Last Modified:05 Nov 2013 16:14

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