A note on Fortʼs theorem

Fortʼs theorem states that if F:X→2Y is an upper (lower) semicontinuous set-valued mapping from a Baire space (X,τ) into the nonempty compact subsets of a metric space (Y,d) then F is both upper and lower semicontinuous at the points of a dense Gδ subset of X. In this paper we show that a variant of...

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Bibliographic Details
Published inTopology and its applications Vol. 160; no. 2; pp. 305 - 308
Main Author Moors, Warren B.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2013
Subjects
Lower semicontinuous
Set-valued mappings
Upper semicontinuous
58C06
Lower semicontinuous
Set-valued mappings
54C60
Upper semicontinuous
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Summary:Fortʼs theorem states that if F:X→2Y is an upper (lower) semicontinuous set-valued mapping from a Baire space (X,τ) into the nonempty compact subsets of a metric space (Y,d) then F is both upper and lower semicontinuous at the points of a dense Gδ subset of X. In this paper we show that a variant of Fortʼs theorem holds, without the assumption of the compactness of the images, provided we restrict the domain space of the mapping to a large class of “nice” Baire spaces.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2012.11.005