Geodesic
Peripheral Covering Properties Imply Covering Properties
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 257-263

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

Recently several papers (11; 12; 13; 14) have been published in which it is shown that a Moore space (normal, in one case) is metrizable if it has the peripheral version (in the sense defined below) of a certain covering property that was known to imply metrizability of Moore spaces. Each of these metrization theorems can be proved more easily by using a slight variation of the appropriate standard proof to show that such a space is collectionwise normal and hence (2, Theorem 10) metrizable. But this approach, as well as that followed in (11 ; 12; 13 ; 14), obscures the point that, in Moore spaces and in more general settings, the peripheral versions of these covering properties imply the covering properties. 
Grace, E. E. Peripheral Covering Properties Imply Covering Properties. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 257-263. doi: 10.4153/CJM-1968-025-8
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