upper semi-continuous

EnglishEdit

Alternative formsEdit

AdjectiveEdit

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 notesEdit

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

Related termsEdit

External linksEdit

Last modified on 18 June 2013, at 18:42