Geodesic
Some Results on the Countable Compactness and Pseudocompactness of Hyperspaces
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1392-1399

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

Let X be a Hausdorff space. Let 2X denote the set of all non-empty closed subsets of X. For a subset A of X, we set 2A = {F 6 2X : F ⊆ A}. Recall that the finite topology on 2X is that topology having as a sub-basis the family {2G : G is open in X} U }2X — 2F : F is closed in X). When endowed with this topology, 2X is referred to as the hyper space of X. For the fundamental properties of hyperspaces, we refer the reader to [6; 7]. Following [6], we adopt the following notation: If A0, A1, ... , An are subsets of X, we set and for all . 
Ginsburg, John. Some Results on the Countable Compactness and Pseudocompactness of Hyperspaces. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1392-1399. doi: 10.4153/CJM-1975-142-9
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