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What does upper semi-continuous mean?

Looking for the meaning or definition of the word upper semi-continuous? Here's what it means.

Adjective
  1. (real-valued) 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.
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