Lets M a set dotted with theT Topology.
It is said that A ⊂ M is compact set if every open cover has a finite subcover, or

A = Un=1An

then, there exist {n1, n2, ..., nm } index such as

A = An1 U An2 U ... U Anm

Note: in Rn; with the usual topology

If A ⊂ Rn is Compact then A is closed and bouded