reserve C for Simple_closed_curve,
  p,q,p1 for Point of TOP-REAL 2,
  i,j,k,n for Nat,
  r,s for Real;

theorem Th1:
  for T being non empty TopSpace, f being continuous RealMap of T,
  A being compact Subset of T holds f.:A is compact
proof
  let T be non empty TopSpace, f be continuous RealMap of T,
  A be compact Subset of T;
  reconsider g = f as continuous Function of T,R^1 by JORDAN5A:27,TOPMETR:17;
  [#](g.:A) is compact by WEIERSTR:9,13;
  hence thesis by WEIERSTR:def 1;
end;
