upper semi-continuous

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English[edit]

Alternative forms[edit]

Adjective[edit]

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.

Usage notes[edit]

  • Both definitions are frequently given, but they are known to be equivalent.

Related terms[edit]

External links[edit]