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Extension of Coverings, of Pseudometrics, and of Linear-Space-Valued Mappings

Published online by Cambridge University Press:  20 November 2018

Richard Arens
Richard Arens*
Affiliation:
University of California
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Let A be a closed subset of a topological space. We show that the following three conditions are equivalent.

1.1 Any countable neighbourhood-finite open covering of A (the topological terms referring to the relative topology of A) has a refinement which can be extended to be a countable neighbourhood-finite open covering of X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 211 - 215
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Arens, R., Extensions of functions on fully normal spaces, Pacific J. Math., 2 (1952), 11–22.Google Scholar
2. Dieudonné, J., Une generalization des espaces compacts, J. Math. Pure Appl., 23 (1944), 65–76.Google Scholar
3. Dowker, C. H., On countably paracompact spaces, Can. J. Math., 3 (1951), 219–224.Google Scholar
4. Hanner, O., Solid spaces and absolute retracts, Ark. Mat. 1 (1951), 375–382.Google Scholar
5. Lefschetz, S., Algebraic topology (Princeton, 1942).Google Scholar
6. Morita, K., On the dimension of normal spaces II, J. Math. Soc. Japan, 2 (1950), 16–33.Google Scholar
7. Stone, A. H., Paracompactness and product spaces, Bull. Amer. Math. Soc, 54 (1948), 677–688.Google Scholar
8. Tukey, J. W., Convergence and uniformity in topology (Princeton, 1951).Google Scholar