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Selections of multivalued maps and shape domination

  • José M. R. Sanjurjo (a1)
Abstract
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.

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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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