Could someone please help me with this question

DEFINITION A set S is said to be compact if whenever it is contained ill a pact iff cover ofs joins of open sets, it is contained in the union of some finite number of the sets in ". If is a family of open sets whose union contains S, then Fis are Subcore called an open cover of S. If & C J and is also an open cover of S, then is called a subcover of S. Thus S is compact iff every open cover of S contains a finite subcover. If S is a compact subset of RR and T is a closed subset of S, Then T is compact. Prove This using the definition of compactness above