Journal of the Mathematical Society of Japan

Generalized Bebutov systems: a dynamical interpretation of shape

Antonio GIRALDO and José M. R. SANJURJO

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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.

Article information

J. Math. Soc. Japan, Volume 51, Number 4 (1999), 937-954.

First available in Project Euclid: 10 June 2008

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Zentralblatt MATH identifier

Primary: 55P55: Shape theory [See also 54C56, 55Q07] 54C56: Shape theory [See also 55P55, 57N25] 54H20: Topological dynamics [See also 28Dxx, 37Bxx] 58F10 58F25

Shape shape morphisms approximative maps Bebutov semidynamical system


GIRALDO, Antonio; M. R. SANJURJO, José. Generalized Bebutov systems: a dynamical interpretation of shape. J. Math. Soc. Japan 51 (1999), no. 4, 937--954. doi:10.2969/jmsj/05140937.

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