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Selections of multivalued maps and shape domination

Published online by Cambridge University Press:  24 October 2008

José M. R. Sanjurjo
José M. R. Sanjurjo
Affiliation:
Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, 28040 Madrid, Spain
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Abstract

Some results are presented which establish connections between shape theory and the theory of multivalued maps. It is shown how to associate an upper-semi-continuous multivalued map F: X → Y to every approximative map f = {fk, X → Y} in the sense of K. Borsuk and it is proved that, in certain circumstances, if F is ‘small’ and admits a selection, then the shape morphism S(f) is generated by a map, and if F admits a coselection then S(f) is a shape domination.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 3 , May 1990 , pp. 493 - 499
Copyright
Copyright © Cambridge Philosophical Society 1990

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