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Connectivity of Function Spaces

Published online by Cambridge University Press:  20 November 2018

Carlos R. Borges
Carlos R. Borges*
Affiliation:
University of California, Davis, California
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Given two spaces X and Y with Y either an AE (metrizable) or ANE (metrizable), little is known with regard to when the function space (Yx, τ), for some topology τ, is an AE (metrizable) or ANE (metrizable) except when very strong separation properties are imposed on X and Y (see [5, pp. 186-189]). One of our tasks will be to eliminate most of these separation property requirements, therefore complementing or extending some of the results of [5]. We also attach an appendix, which contains some needful information, as well as the complete local analogue of [2, Theorem 5.1].

Throughout, we use either the terminology and notation of [2] or of the appendix. We also let co stand for the compact-open topology and pc stand for the pointwise convergence topology of any function space

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 759 - 763
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Arens, R. and Dugundji, J., Topologies for function spaces, Pacific J. Math. 1 (1951), 5–31.Google Scholar
2. Borges, C. R., A study of absolute extensor spaces, Pacific J. Math. 31 (1960), 609–617.Google Scholar
3. Dieudonne, J., Une generalization des espaces compacts, J. Math. Pures Appl. 23 (1944), 65–76.Google Scholar
4. Hanner, O., Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat. 2 (1952), 315–360.Google Scholar
5. Hu, S. T., Theory of Retracts (Wayne State University Press, Detroit, 1965).Google Scholar
6. Michael, E. A., Some extension theorems for continuous functions, Pacific J. Math. 3 (1953), 789–806.Google Scholar
7. Chou, Sho-Kwan, On the Borsuk absolute homotopy extension property, Amer. Math. Soc. Transi, (ser. 2), 38 (1964), 291–300.Google Scholar