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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A necessary and sufficient condition
for upper hemicontinuous
set-valued mappings without compact-values being upper demicontinuous


Authors: Gan-Shang Yang and George Xian-Zhi Yuan
Journal: Proc. Amer. Math. Soc. 126 (1998), 3539-3544
MSC (1991): Primary 47H04, 54C60
MathSciNet review: 1628436
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Abstract: The purpose of this article is to give a characterization of an upper hemicontinuous mapping with non-empty convex values being upper demicontinuous, i.e., we show that an upper hemicontinuous set-valued mapping with non-empty convex values (not necessarily compact-valued) is upper demicontinuous if and only if the set-valued mapping has no interior asymptotic plane.


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Additional Information

Gan-Shang Yang
Affiliation: Department of Mathematics, Yunnan National Institute, Kunming, China 650031

George Xian-Zhi Yuan
Affiliation: Department of Mathematics, The University of Queensland, Brisbane, Queensland, Australia 4072
Email: xzy@maths.uq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-98-05082-5
PII: S 0002-9939(98)05082-5
Keywords: Upper semicontinuous, upper hemicontinuous, upper demicontinuous, asymptotic plane, interior asymptotic plane
Received by editor(s): February 26, 1997
Additional Notes: This project was supported in part by the Australian Research Council.
Communicated by: David R. Larson
Article copyright: © Copyright 1998 American Mathematical Society