Normality and paracompactness of the Fell topology

Holá, L’.; Levi, S.; Pelant, J.

doi:10.1090/S0002-9939-99-04737-1

Normality and paracompactness of the Fell topology
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by L’. Holá, S. Levi and J. Pelant PDF

Proc. Amer. Math. Soc. 127 (1999), 2193-2197 Request permission

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 Lindelöf and locally compact. For the Fell topology normality, paracompactness and Lindelöfness are equivalent.

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