Convexity/The diameter of a set

From Wikibooks, open books for an open world
Jump to navigation Jump to search

If a distance measure between any two points, d(A,B), is defined on a space, and X is a set in this space, then the diameter D(X) is the supremum of d(A,B) over all points A, B in X.

Theorem: in Euclidean space, D(H(X)) = D(X).