On normality of the Wijsman topology

Let ( X , ρ ) be a metric space and ( CL ( X ), W ρ ) be the hyperspace of all nonempty closed subsets of X equipped with the Wijsman topology. The Wijsman topology is one of the most important classical hyperspace topologies. We give a partial answer to a question posed in Di Maio (Quaderni di Mate...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2013-06, Vol.192 (3), p.349-359
Main Authors: Holá, L’ubica, Novotný, Branislav
Format: Article
Language:English
Subjects:
Hyperspaces
Mathematics
Mathematics and Statistics
Metric space
Normality
Topology
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Summary:Let ( X , ρ ) be a metric space and ( CL ( X ), W ρ ) be the hyperspace of all nonempty closed subsets of X equipped with the Wijsman topology. The Wijsman topology is one of the most important classical hyperspace topologies. We give a partial answer to a question posed in Di Maio (Quaderni di Matematica, 3:55–92, 1998 ) whether the normality of ( CL ( X ), W ρ ) is equivalent to its metrizability. If ( X , ρ ) is a linear metric space, then ( CL ( X ), W ρ ) is normal if and only if ( CL ( X ), W ρ ) is metrizable. Some further results concerning normality of the Wijsman topology on CL ( X ) are also proved.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-011-0227-9