We give characterizations for a subspace of a hyperspace, endowed with either the Vietoris or the Wijsman topology, to be compact or relatively compact. Then we characterize-both globally and at the single points-the local compactness of a hyperspace, endowed with either the Vietoris, the Wijsman, or the Hausdorff metric topology. Several examples illustrating the behaviour of local compactness are also included. © 2001 Elsevier Science B.V. All rights reserved.
Costantini, C., Levi, S., Pelant, J. (2002). Compactness and local compactness in hyperspaces. TOPOLOGY AND ITS APPLICATIONS, 123(3), 573-608 [10.1016/S0166-8641(01)00222-X].
Compactness and local compactness in hyperspaces
LEVI, SANDRO;
2002
Abstract
We give characterizations for a subspace of a hyperspace, endowed with either the Vietoris or the Wijsman topology, to be compact or relatively compact. Then we characterize-both globally and at the single points-the local compactness of a hyperspace, endowed with either the Vietoris, the Wijsman, or the Hausdorff metric topology. Several examples illustrating the behaviour of local compactness are also included. © 2001 Elsevier Science B.V. All rights reserved.
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