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green) above its graph (in blue), is a convex set. let s be a vector space or an affine space over the real numbers , or, more generally, over some ordered field . this includes euclidean spaces, which are affine spaces. a subset c of s is convex if, for all x and y in c, the line segment connecting
x and y is included in c. this means that the affine combination ( − t)x + ty belongs to c, for all x and y in c, and t in the interval [ , ]. this implies that convexity (the property of being convex) is invariant under affine transformations . this implies also that a convex set in a real or complex...
https://en.wikipedia.org/wiki/Convex_set
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