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

Antonio GIRALDO and José M. R. SANJURJO
Source: J. Math. Soc. Japan Volume 51, Number 4 (1999), 937-954.

#### 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.

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Primary Subjects: 55P55, 54C56, 54H20, 58F10, 58F25
Full-text: Open access