reserve n for Element of NAT,
        x for Element of COMPLEX n;
reserve p,q for Point of the_Complex_Space n,
  V for Subset of the_Complex_Space n;

theorem Th5:
  for A being Subset of COMPLEX n st A = V holds A is closed iff V is closed
proof
  let A be Subset of COMPLEX n;
  assume A = V;
  then [#](the_Complex_Space n) \ V is open iff A` is open by Th4;
  hence thesis by SEQ_4:132;
end;
