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Selections of multivalued maps and shape domination

Published online by Cambridge University Press:  24 October 2008

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

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: XY to every approximative map f = {fk, XY} 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
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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