## Journal of the Mathematical Society of Japan

### Generalized Bebutov systems: a dynamical interpretation of shape

#### 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 in Project Euclid: 10 June 2008

http://projecteuclid.org/euclid.jmsj/1213107829

Digital Object Identifier
doi:10.2969/jmsj/05140937

Mathematical Reviews number (MathSciNet)
MR1705255

Zentralblatt MATH identifier
1033.55007

#### Citation

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. http://projecteuclid.org/euclid.jmsj/1213107829.