A subset $B$ of a <metric space> is <bounded set>[bounded] if it lies in some ball of finite radius: there are $x_0$ in the space and $R<\infty$ with $d(x,x_0)\leq R$ for every $x\in B$. For a nonempty subset, this is equivalent to finite <diameter>, $\sup_{x,y\in B}d(x,y)<\infty$. The empty subset is bounded by convention.

Solution

Past exam of the options II course of the University of Oxford / 2010 / E / E4 / a / ii / Solution

 Solution (source code)