Hemicontinuity of Correspondences: Examples

Prof. Mark Walker, University of Arizona
We study several correspondences to determine whether they are upper or lower hemicontinuous or not. We emphasize the importance of a correspondence being closed-valued, and we consider singleton-valued correspondences.

A great reference for the continuity properties of correspondences is Kim Border's book "Fixed Point Theorems with Applications to Economics and Game Theory." Also see Rangarajan Sundaram's "A First Course in Optimization Theory."

[mentalcrafter]

Thank you for the clear examples. Helped me understand what hemicontinuity actually is! Much love from Serbia 🏳️‍🌈

[youshengtang]

Thank you for this great video. But for the 5:11 example, if we pick a point, really close to 0.5, but on the right-hand side of 0.5, then we move to the left, then the whole interval [.3, .7] suddenly appear, right? Did I use the concluded intuition wrong, or this actually makes this point not UHC?

[hahayuer]

appreciate for the clear description regarding continuity of correspondence. However, I really hope a formal definition regarding closed valued continuity could be provided