Hemicontinuity is a concept from the field of mathematical analysis, specifically within the study of functions and topology. It describes a type of continuity for set-valued functions (or multivalued functions), which associate each point in a domain with a set of values rather than a single value.
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For a real Banach space and a convex set , a map is hemicontinuous if is continuous on for all and . This tests continuity only along line segments and only through pairings with fixed vectors. It is enough for the limiting step in Minty's lemma.