 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2010/e/e4/a/ii/solution

B

of a metric space is 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.

 New to topics? Read the docs here!