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On m-Paracompact Spaces and ω-Mappings

Published online by Cambridge University Press:  20 November 2018

T. E. Gantner
T. E. Gantner*
Affiliation:
University of Dayton, Dayton Ohio
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The purpose of this note is to present a characterization of m-paracompact normal spaces in terms of ω-mappings into m-separable metric spaces; this result is almost contained in Morita's original paper [2] and is implicitly contained in Shapiro's thesis paper [5].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 427 - 428
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Michael, E., A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (1953), 831–838.Google Scholar
2. Morita, K., Paracompactness and product spaces, Fund. Math. 50 (1962), 223–236.Google Scholar
3. Pareek, C. M., On spaces and co-mappings, Canad. Math. Bull. 14 (1971), 455–457.Google Scholar
4. Ponomarev, V. I., On paracompact and finally compact spaces, Soviet Math. Dokl. 2 (1961), 1510–1512.Google Scholar
5. Shapiro, H. L., Extensions of pseudometrics, Canad. J. Math. 18 (1966), 981–998.Google Scholar
6. Stone, A. H., Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977-982.Google Scholar
7. Tukey, J. W., Convergence and uniformity in topology, Princeton Univ. Press, Princeton, N. J. 1940.Google Scholar
8. Willard, S., General Topology, Addison-Wesley, Reading, Mass., 1970.Google Scholar