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On Spaces and ω-Mappings

Published online by Cambridge University Press:  20 November 2018

C. M. Pareek
C. M. Pareek*
Affiliation:
University of Saskatchewan, Regina, Saskatchewan
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This note is closely related, as far as methods are concerned, to [3]. In [3] Ponomarev established “In order for a regular space X to be Lindelöf, it is necessary and sufficient that for each open covering ω of the space X there exists an ω-mapping ƒ:X → Y onto some separable metric space Y.” It is the purpose of this note to show that if the word “countable (or finite)” is inserted in the proper place we can obtain an analogous characterization for normal countably paracompact (or normal) spaces.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 455 - 457
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955.Google Scholar
2. Mansfield, M. J., On countably paracompact normal spaces, Canad. J. Math. 9 (1957), 443-449.Google Scholar
3. Ponomarev, V. I., On paracompact and finally compact spaces, Soviet Math. Dokl. 2 (1961), 1510-1512.Google Scholar