|
|||||
|
|
Normal Vietoris Implies Compactness: A Short Proof |
|
| Authors: | G Di Maio E Meccariello S Naimpally |
| Institution: | (1) Facoltà di Scienze, Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Via Vivaldi 43, 81100 Caserta, Italia;(2) Facoltà di Ingegneria, Università del Sannio, Piazza Roma, Palazzo B. Lucarelli, 82100 Benevento, Italia;(3) 96 Dewson Street, Toronto, Ontario, M6H 1H3, Canada |
| Abstract: | One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities. |
| Keywords: | hyperspaces Vietoris topology locally finite topology Hausdorff metric compactness normality countable compactness |
| 本文献已被 SpringerLink 等数据库收录！ | |