Example of a Totally Bounded Metric Space
Let
be a subset of a metric space
and let
An
- net fo
is a finite set of points in
such that for each
for some
More intuitively, every
is less thanfrom some
If an- net exists for every
thenis totally bounded.
Now letAn- net for a circle with centre
radius 1, can be written
We can choose the- net to be the set of points
and this set contains at most
points.
