We characterize the separable complete ultrametric spaces whose Wijsman hyperspace admits a continuous selection; such an investigation is closely connected to a similar result of V. Gutev about the Ball hyperspace. The characterization may be obtained in terms of a suitable property either of the base space (X, d) (condition (#)) or of the Wijsman hyperspace itself (total disconnectedness). We also give a necessary and sufficient condition for the zero-dimensionality of the Wijsman hyperspace of a (separable) ultrametric space, and we provide an example where such a hyperspace turns out to be connected. © 1998 Elsevier Science B.V. All rights reserved.

Bertacchi, D., Costantini, C. (1998). Existence of selections and disconnectedness properties for the hyperspace of an ultrametric space. TOPOLOGY AND ITS APPLICATIONS, 88(3), 179-197.

Existence of selections and disconnectedness properties for the hyperspace of an ultrametric space

BERTACCHI, DANIELA;
1998

Abstract

We characterize the separable complete ultrametric spaces whose Wijsman hyperspace admits a continuous selection; such an investigation is closely connected to a similar result of V. Gutev about the Ball hyperspace. The characterization may be obtained in terms of a suitable property either of the base space (X, d) (condition (#)) or of the Wijsman hyperspace itself (total disconnectedness). We also give a necessary and sufficient condition for the zero-dimensionality of the Wijsman hyperspace of a (separable) ultrametric space, and we provide an example where such a hyperspace turns out to be connected. © 1998 Elsevier Science B.V. All rights reserved.
Articolo in rivista - Articolo scientifico
Ultrametric space
English
179
197
Bertacchi, D., Costantini, C. (1998). Existence of selections and disconnectedness properties for the hyperspace of an ultrametric space. TOPOLOGY AND ITS APPLICATIONS, 88(3), 179-197.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18170
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