 The metric generated by this norm is called the Chebyshev metric, after Pafnuty Chebyshev, who was first to systematically study it.If we allow unbounded functions, this formula does not yield a norm or metric in a strict sense, although the obtained so-called extended metric still allows one to define a topology on the function space in question.If "f" is a continuous function on a closed interval, or more generally a compact set, then it is bounded and the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum.