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Locally trivial homotopy functors and their domain of representation

Published online by Cambridge University Press:  09 April 2009

Michael D. Alder
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, W. A. 6009.
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Abstract

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The well known theorem of E. H. Brown on the representation of Homotopy Functors is extended to a larger domain category. This is accomplished by requiring the functor to satisfy a further condition, that of being locally trivial: the condition is both necessary and sufficient for the extension and is satisfied by functors arising from locally trivial fibre bundles such as K-theory.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Brown, E. H. (1965), ‘Abstract Homotopy Theory’, Trans. Am. Math. Soc. 119, 7985.CrossRefGoogle Scholar
Freyd, P. (1964), ‘Abelian Categories’, Harper and Row.Google Scholar
Spanier, E. (1966), ‘Algebraic Topology’, McGraw-Hill.Google Scholar
Eckmann, B. and Hilton, P. (1963/1964), ‘Unions and Intersections in Homotopy Theory’, Comm. Math. Helv. 38, 293307.CrossRefGoogle Scholar
Dold, A. (1963), ‘Partitions of Unity in the theory of Fibrations’, Ann. Math. 78, 223255.CrossRefGoogle Scholar
Dold, A. (1966), ‘Halbexakte Homotopiefunktoren’, Springer Lecture Note Series No. 12.Google Scholar