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Density and finiteness. A discrete approach to shape

Giraldo, A. and Rodríguez Sanjurjo, José Manuel (1997) Density and finiteness. A discrete approach to shape. Topology and its Applications, 76 (1). pp. 61-77. ISSN 0166-8641

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Abstract

We show in this paper that the category of shape can be modelled in discrete terms using maps defined in dense subsets of compacta. This approach to shape provides in addition a characterization of the shape of compacta which does not require external elements and uses only continuous single-valued functions, in contrast with the existing internal characterizations of shape. As an application, we prove a connection between the notion of shape image, due to Lisica, and the basic notion of omega limit of a dynamical system.

Item Type:Article
Uncontrolled Keywords:Density: Discrete map: Shape category; Shape image: Omega limit: Lyapunov stability
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16962
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