Geodesic
On Expanding Locally Finite Collections
Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 58-68

Voir la notice de l'article provenant de la source Cambridge University Press

A space X is in-expandable, where m is an infinite cardinal, if for every locally finite collection {Hα| α ∈ A} of subsets of X with |A| ≦ m(cardinality of A ≦ m) there exists a locally finite collection of open subsets {Gα| α ∈ A} such that Hα ⊆ Gα for every α ∈ A. X is expandable if it is m-expandable for every cardinal m. The notion of expandability is closely related to that of collection wise normality introduced by Bing [1], X is collectionwise normal if for every discrete collection of subsets {Hα|α ∈ A} there is a discrete collection of open subsets {Gα|α ∈ A} such that Hα ⊆ Gα for every α ∈ A. Expandable spaces share many of the properties possessed by collectionwise normal spaces. For example, an expandable developable space is metrizable and an expandable metacompact space is paracompact. 
On Expanding Locally Finite Collections. Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 58-68. doi: 10.4153/CJM-1971-006-3
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