reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem
  for P being Subset of TOP-REAL2 st P is bounded holds UBD P is not bounded
proof
  let P be Subset of TOP-REAL2;
  assume P is bounded;
  then UBD P is_outside_component_of P by JORDAN2C:68;
  hence thesis by JORDAN2C:def 3;
end;
