Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Selections of multivalued maps and shape domination

José M. R. Sanjurjoa1

a1 Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, 28040 Madrid, Spain


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.

(Received May 09 1989)