A Theorem about Compact Spaces in Topology, a branch, out of eleven, of mathematics. A Theorem about Compact Spaces in Topology, a branch, out of eleven, of mathematics.

A discrete topology on the integers, Z, is defined by letting every subset of Z be open If that is true then Z is a discrete topological space and it is equipped with a discrete topology.

Now is it compact?

We know that a discrete space is compact if and only if it is finite. Clearly Z is not finite, so the answer is no. If you picked a finite field such a Z7 ( integers mod 7) then the answer would be yes.

Any closed bounded subset of a metric space is compact.

Ring topology is the passive topology in computer networks