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Normality and paracompactness of the Fell topology
Author(s):
L'.
Holá;
S.
Levi;
J.
Pelant
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2193-2197.
MSC (1991):
Primary 54B20
Posted:
March 1, 1999
MathSciNet review:
1485480
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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.
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Additional Information:
L'.
Holá
Affiliation:
Mathematical Institute, Slovak Academy of Sciences, Stefániková 49 Bratislava, Slovakia
Email:
hola@mau.savba.sk
S.
Levi
Affiliation:
Dipartimento di Matematica, Universita di Milano, Via C. Saldini 50, 20133 Milano, Italy
Email:
slevi@vmimat.mat.unimi.it
J.
Pelant
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Praha, Czech republic
Email:
pelant@beba.cesnet.cz
DOI:
10.1090/S0002-9939-99-04737-1
PII:
S 0002-9939(99)04737-1
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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