boundedBounded2002-01-01 22:58:072008-06-18 20:18:16Definition\usepackage{amssymb}
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\usepackage{xypic}Given a metric space $(X, d)$, a subset $A\subseteq X$ is said to be \emph{bounded} if there is some positive real number $M$ such that $d(x, y)\leq M$ whenever $x, y \in A$.
A function $f : X \rightarrow Y$ from a set $X$ to a metric space $Y$ is said to be \emph{bounded} if its range is bounded in $Y$.