Example of a Totally Bounded Metric Space

Letbe a subset of a metric spaceand letAn- net fois a finite set of points insuch that for eachfor some More intuitively, everyis less thanfrom someIf an- net exists for everythenis totally bounded.

Now letAn- net for a circle with centreradius 1, can be written

We can choose the- net to be the set of pointsand this set contains at mostpoints.