The Shrinking Property
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 385-388
Voir la notice de l'article provenant de la source Cambridge University Press
A space has the shrinking property if, for every open cover {Va | a ∈ A}, there is an open cover {Wa | a ∈ A} with for each a ∈ A.lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property.
Rudin, Mary Ellen. The Shrinking Property. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 385-388. doi: 10.4153/CMB-1983-064-x
@article{10_4153_CMB_1983_064_x,
author = {Rudin, Mary Ellen},
title = {The {Shrinking} {Property}},
journal = {Canadian mathematical bulletin},
pages = {385--388},
year = {1983},
volume = {26},
number = {4},
doi = {10.4153/CMB-1983-064-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-064-x/}
}
[1] 1. Dowker, C. H., On countably paracompact spaces, Can. J. Math. 3 (1971) 214-224. Google Scholar
[2] 2. Rudin, M. E., A normal space X for which X×I is not normal, Fund. Math. LXXIII (1971) 179-186. Google Scholar
[3] 3. Rudin, M. E., K-Dowker spaces, Czech. Math. J. 28 (1978) Praha, 324-326. Google Scholar
[4] 4. Gul'ko, S. P., On properties of subsets of ∑-products, Soviet Math. Dokl. 18 (1977), 1438-1442. Google Scholar
[5] 5. LeDonne, A., Normality and shrinking property in ∑-product of spaces, this Journal, to appear. Google Scholar
Cité par Sources :