upper semi-continuous

• upper semicontinuous

upper semi-continuous (not comparable)

1. (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.
2. (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.

• lower semi-continuous

• upper semi-continuous on Wikipedia.Wikipedia