On Spaces and ω-Mappings
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 455-457
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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.
Pareek, C. M. On Spaces and ω-Mappings. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 455-457. doi: 10.4153/CMB-1971-083-x
@article{10_4153_CMB_1971_083_x,
author = {Pareek, C. M.},
title = {On {Spaces} and {\ensuremath{\omega}-Mappings}},
journal = {Canadian mathematical bulletin},
pages = {455--457},
year = {1971},
volume = {14},
number = {3},
doi = {10.4153/CMB-1971-083-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-083-x/}
}
[1] 1. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955. Google Scholar
[2] 2. Mansfield, M. J., On countably paracompact normal spaces, Canad. J. Math. 9 (1957), 443-449. Google Scholar
[3] 3. Ponomarev, V. I., On paracompact and finally compact spaces, Soviet Math. Dokl. 2 (1961), 1510-1512. Google Scholar
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