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.
Bertacchi, D; Costantini, C
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/18170
Citazioni
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
Social impact