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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 note on intersection of lower semicontinuous multifunctions


Authors: Alojzy Lechicki and Andrzej Spakowski
Journal: Proc. Amer. Math. Soc. 95 (1985), 119-122
MSC: Primary 54C60; Secondary 46N05, 90C48
MathSciNet review: 796459
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Abstract: Let $ {F_1}$ and $ {F_2}$ be closed and convex valued multifunctions from a topological space $ X$ to a normed space $ Y$. Assume that the multifunctions are lower semicontinuous at $ {x_0}$. We proof that the intersection multifunction $ F = {F_1} \cap {F_2}$ is lower semicontinuous at $ {x_0}$ provided $ F({x_0})$ is bounded and has nonempty interior.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0796459-2
PII: S 0002-9939(1985)0796459-2
Keywords: Multifunction, lower semicontinuity, intersection of multifunctions
Article copyright: © Copyright 1985 American Mathematical Society