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.
|Uncontrolled Keywords:||Density: Discrete map: Shape category; Shape image: Omega limit: Lyapunov stability|
|Subjects:||Sciences > Mathematics > Geometry|
Sciences > Mathematics > Topology
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|Deposited On:||31 Oct 2012 10:44|
|Last Modified:||07 Feb 2014 09:39|
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