upper semicontinuous function

upper semicontinuous function

[′əp·ər ¦sem·i·kən′tin·yə·wəs ′fəŋk·shən] (mathematics) A real-valued function ƒ(x) is upper semicontinuous at a point x0 if, for any small positive ε, ƒ(x) always is less than ƒ(x0) + ε for all x in some neighborhood of x0.