Geodesic
Hyperspaces of H-Closed Spaces
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1072-1079

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

A space is H(i) [R(i)] if every open [regular] filter base has a cluster point and H(ii) [R(ii)] if every open [regular] filter base with a unique cluster point converges. This terminology is due to C. T. Scarborough and A. H. Stone [11]; H(i) spaces have been studied as quasi-H-closed spaces in [10] and as generalized absolutely closed spaces in [6]. Hausdorff H(i) [H(ii)] spaces are called H-closed [minimal Hausdorff] and regular T1 R(i) [R(ii)] spaces are called R-closed [minimal regular]. For a space X, 2X is the set of all non-empty closed subsets of X with the finite topology [8]. The present study was motivated by the longstanding problem of whether or not a T 3 space with every closed subset R-closed is compact, and also by the well-known result ([8] and [14]) that X is compact if and only if 2X is compact. 
Friedler, L. M.; Jr., R. F. Dickman; Krystock, R. L. Hyperspaces of H-Closed Spaces. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1072-1079. doi: 10.4153/CJM-1980-082-x
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