What is "upper semi-continuous"

a. 1 (context of a real-valued function on a topological space English) Such that, for each fixed number, the subspace of points whose images are at least that number is closed. 2 (context of a real-valued function on a topological space English) Such that for each fixed point ''x'' there is some neighborhood whose image's limit superior is ''x'''s image. alt. 1 (context of a real-valued function on a topological space English) Such that, for each fixed number, the subspace of points whose images are at least that number is closed. 2 (context of a real-valued function on a topological space English) Such that for each fixed point ''x'' there is some neighborhood whose image's limit superior is ''x'''s image.