The property of this name says that any open covering can be expressed as a finite subcovering.
The property of this name says that any open covering can be expressed as a finite subcovering. The theorem of the name can be proved by first proving that, for a metric space A (or a subset of a metric space), any arbitrary sequence has a limit point in A. Next, one must prove that every open cover has a finite subcover. Alternatively, for the real numbers, one could work from the Bolzano-Weierstrass theorem and prove – for ten points– what theorem that states that a set is compact if and only if it is closed and bounded?
The property of this name says that any open covering can be expressed as a finite subcovering.
Heine-Borel theorem