upper semicontinuous function

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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 pointx₀if, for any small positive ε, ƒ(x) always is less than ƒ(x₀) + ε for allxin some neighborhood ofx₀.

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