reserve C for Simple_closed_curve,
  P for Subset of TOP-REAL 2,
  p for Point of TOP-REAL 2,
  n for Element of NAT;

theorem
  for A being Subset of the carrier of TOP-REAL 2 holds UBD A misses A
proof
  let A be Subset of the carrier of TOP-REAL 2;
  UBD A c= A` by JORDAN2C:26;
  hence thesis by XBOOLE_1:63,79;
end;
