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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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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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