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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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.

Article information

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

Dates
First available: 10 June 2008

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1213107829

Digital Object Identifier
doi:10.2969/jmsj/05140937

Mathematical Reviews number (MathSciNet)
MR1705255

Zentralblatt MATH identifier
1033.55007

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

Keywords
Shape shape morphisms approximative maps Bebutov semidynamical system

Citation

GIRALDO, Antonio; M. R. SANJURJO, José. Generalized Bebutov systems: a dynamical interpretation of shape. Journal of the Mathematical Society of Japan 51 (1999), no. 4, 937--954. doi:10.2969/jmsj/05140937. http://projecteuclid.org/euclid.jmsj/1213107829.


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