upper semi-continuous

== English == === Alternative forms === upper semicontinuous === Adjective === upper semi-continuous (not comparable) (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. (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 ==== Both definitions are frequently given, but they are known to be equivalent. ==== Related terms ==== lower semi-continuous ==== Translations ==== ==== Further reading ==== upper semi-continuous on Wikipedia.Wikipedia