Question: Show that a closed correspondence is closed-valued
Our next result shows that closedness is closely related to upper hemicontinuity. Because closedness is also fairly easy to check in many cases, a convenient way to show that a given correspondence is uhc is to establish its closedness and then apply Theorem 11.6.
Theorem: Relationship between closedness and upper hemicontinuity. Let f.→ →Y be a nonempty valued and closed correspondence. If for any bounded set B in X the image set Ψ(B) is bounded, then Ψ is uhc.