Could someone please help me with this question

1 DEFINITION A set S is said to be compact if whenever it is contained in the union of pact iff cover ofSims 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 Ice Subcover called an open cover of S. If & C 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