Definition from Wiktionary, the free dictionary
See also: upper semicontinuous
- (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.
- Both definitions are frequently given, but they are known to be equivalent.