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Normality and paracompactness of the Fell topology |
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| Authors: | L'. Holá S. Levi J. Pelant |
| Affiliation: | Mathematical Institute, Slovak Academy of Sciences, Stefániková 49 Bratislava, Slovakia ; Dipartimento di Matematica, Universita di Milano, Via C. Saldini 50, 20133 Milano, Italy ; Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Praha, Czech republic |
| Abstract: | Let  be a Hausdorff topological space and  the hyperspace of all closed nonempty subsets of  . We show that the Fell topology on  is normal if and only if the space  is Lindelöf and locally compact. For the Fell topology normality, paracompactness and Lindelöfness are equivalent. |
| Keywords: | Fell topology, locally compact Hausdorff space, Lindel" {o}f space, normal space, $sigma $-compact |
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