Suppose that $X,Y$ are compact metric spaces, and $g:X\rightarrow Y$ is a multivalued mapping that is both upper and lower hemicontinuous. Is there a single valued continuous selection of $g$? If it helps, $X$ and $Y$ are compact subsets of finite dimensional normed spaces, but $g(x)$ is not convex, in general.
$\begingroup$
$\endgroup$
1
-
$\begingroup$ Since Michael's theorem does not apply, is there some other well known result in set-valued analysis that covers this situation? A reference would be greatly appreciated. $\endgroup$– Brian LinsCommented Aug 7, 2012 at 19:23
Add a comment
|