Let X be a Hausdorff topological space and CL(X) the hyperspace of all closed nonempty subsets of X. We show that the Fell topology on CL(X) is normal if and only if the space X is Lindelof and locally compact. For the Fell topology normality, paracompactness and Lindelofness are equivalent
Holà, L., Levi, S., Pelant, J. (1999). Normality and paracompactness of the Fell topology. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 127(7), 2193-2197 [10.1090/S0002-9939-99-04737-1].
Normality and paracompactness of the Fell topology
Levi, S;
1999
Abstract
Let X be a Hausdorff topological space and CL(X) the hyperspace of all closed nonempty subsets of X. We show that the Fell topology on CL(X) is normal if and only if the space X is Lindelof and locally compact. For the Fell topology normality, paracompactness and Lindelofness are equivalent
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