Definitions from Wiktionary (upper semi-continuous)

▸ adjective:  (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.
▸ adjective:  (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.



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