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On the hyperspace of a non-separable metric space |
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| Authors: | Camillo Costantini |
| Affiliation: | Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy |
| Abstract: | We prove the following two results. 1) There exists a non-separable complete metric space whose Wijsman hypertopology is not Cech-complete. 2) There exist a non-separable metrizable space and two compatible metrics on it, such that the collections of the Borel sets generated by the relative Wijsman hypertopologies do not coincide. |
| Keywords: | Non-separable metric space Wijsman hypertopology v{C}ech-completeness Borel sets |
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