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Normality and paracompactness
of the Fell topology

Authors: L'. Holá, S. Levi and J. Pelant
Journal: Proc. Amer. Math. Soc. 127 (1999), 2193-2197
MSC (1991): Primary 54B20
Published electronically: March 1, 1999
MathSciNet review: 1485480
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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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Additional Information

L'. Holá
Affiliation: Mathematical Institute, Slovak Academy of Sciences, Štefániková 49 Bratislava, Slovakia

S. Levi
Affiliation: Dipartimento di Matematica, Universita di Milano, Via C. Saldini 50, 20133 Milano, Italy

J. Pelant
Affiliation: Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha, Czech republic

Keywords: Fell topology, locally compact Hausdorff space, Lindel\"{o}f space, normal space, $\sigma $-compact
Received by editor(s): February 12, 1997
Received by editor(s) in revised form: October 7, 1997
Published electronically: March 1, 1999
Additional Notes: The third author was partially supported by the grant GACR 201/94/0069 and the grant 119 401 of Acad. Sci. CR
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society