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Generalized Bebutov systems: a dynamical interpretation of shape

Giraldo, A. and Rodríguez Sanjurjo, José Manuel (1999) Generalized Bebutov systems: a dynamical interpretation of shape. Journal of the mathematical society of japan, 51 (4). pp. 937-954. ISSN 0025-5645

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Abstract

We define a semidynamical system - inspired by some classical dynamical systems studied by Bebutov in function spaces - in the space of approximative maps A(X, Y) between two metric compacta, with a suitable metric. Shape and strong shape morphisms are characterized as invariant subsets of this system. We study their structure and asymptotic properties and use the obtained results to give dynamical characterizations of basic notions in shape theory, like trivial shape, shape domination by polyhedra and internal FANRs.

Item Type:Article
Uncontrolled Keywords:Shape, shape morphisms, approximative maps, Bebutov semidynamical system
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16899
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