Geodesic
Directed Covers and Paracompact Spaces
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 649-654

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

A cover is directed (is well-ordered, totally ordered) if it is directed (is well-ordered, totally ordered, respectively) by set inclusion. Specifically is directed if, given U, V in , there exists W in such that U ⋃ V ⊂ W.Directed covers have been used implicitly in numerous theorems dealing with paracompactness and related properties. In particular, characterizations of paracompactness in terms of product spaces seem to require the use of directed covers (3; 11, §2; or 12). However, the utility of directed covers has not been fully exploited. 
Mack, John. Directed Covers and Paracompact Spaces. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 649-654. doi: 10.4153/CJM-1967-059-0
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