A counterexample on the semicontinuity of minima
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- by Fernando Luque-Vásquez and Onésimo Hernández-Lerma PDF
- Proc. Amer. Math. Soc. 123 (1995), 3175-3176 Request permission
Abstract:
Let X and Y be metric spaces, $\Phi$ a multifunction from X to Y, and v a real-valued function on $X \times Y$. We give an example in which $\Phi$ is continuous, and v is continuous, inf-compact and bounded below, but the minimum function ${v^ \ast }(x): = {\inf _{y \in \Phi (x)}}v(x,y)$ on X is not lower semicontinuous.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3175-3176
- MSC: Primary 49J45; Secondary 49K40
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301515-2
- MathSciNet review: 1301515