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Selections of multivalued maps and shape domination

  • José M. R. Sanjurjo (a1)

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.

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[5] Z. Ĉerin . Homotopy properties of locally compact spaces at infinity-calmness and smoothness. Pacific J. Math. 79 (1978), 6991.

[7] Z. Ĉerin and T. Watanabe . Borsuk fixed point theorem for multivalued maps. In Geometric Topology and Shape Theory (eds. S. Mardešić and J. Segal ), Lecture Notes in Math. vol. 1283 (Springer-Verlag, 1987), pp. 3037.

[8] J. Dydak and J. Segal . Shape Theory: An Introduction. Lecture Notes in Math. vol. 688 (Springer-Verlag, 1978).

[9] W. E. Haver . A covering property for metric spaces. In Proceedings of Topology Conference (eds. R. F. Dickman and P. Hatcher ), Lectures Notes in Math. vol. 375 (Springer-Verlag1974), pp. 108113.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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