theorem
  for A being Subset of COMPLEX n st A = COMPLEX n holds A is open
proof
  let A be Subset of COMPLEX n;
  assume
A1: A = COMPLEX n;
  let x such that
  x in A;
   reconsider j=1 as Element of REAL by NUMBERS:19;
  take j;
  thus 0 < j;
  let z such that
  |.z.| < j;
  thus thesis by A1;
end;
