## upper-semi-continuous

Adjective

(*not comparable*)

- (of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at least that number is closed.
- (of a real-valued function on a topological space) Such that for each fixed point
*x*there is some neighborhood whose image's limit superior is*x*'s image.

Usage notes

- Both definitions are frequently given, but they are known to be equivalent.