ON THE INFIMUM OF THE HAUSDORFF AND VIETORIS TOPOLOGIES

Authors
LEVI S LUCCHETTI R PELANT J
Citation
S. Levi et al., ON THE INFIMUM OF THE HAUSDORFF AND VIETORIS TOPOLOGIES, Proceedings of the American Mathematical Society, 118(3), 1993, pp. 971-978
Citations number
11
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
118
Issue
3
Year of publication
1993
Pages
971 - 978
Database
ISI
SICI code
0002-9939(1993)118:3<971:OTIOTH>2.0.ZU;2-0
Abstract
We study the infimum of the Hausdorff and Vietoris topologies on the h yperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or i s a UC space.