Normed spaces

normed vector space that is complete

vector space on which a distance is defined

real or complex vector space with an additional structure called an inner product

function spaces generalizing finite-dimensional p norm spaces

distance between vectors or points computed as the pth root of the sum of pth powers of coordinate differences

lemma

p-norm for p equal to ∞

normed vector space for which the closed unit ball is strictly convex

theorem