By using the definition of a compact set in R, show that a closed subset X of a compact set K is compact.

Question

anonymous · Answer

haha good luck! :P

anonymous · Answer

what is your definition of compact?  every open cover can be reduced to finite sub cover?

anonymous · Answer

if so, proof is not hard, and doesn't even depend on being in R
your set $A$ s closed inside of a compact set C.  if your open cover of is say $\cup O_\beta$ then $\cup O_\beta \cup A-C$ is an open cover of C and therefore can be reduced to a finite sub-cover.

anonymous · Answer

Definition : A subset A of R is compact if every opening covering of A contains a finite subcovering of A

anonymous · Answer

ok then proof above should work right?

anonymous · Answer

noting of course that $A-C$ is open since C is closed.