reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;

theorem Th55:
  for A being Subset of TopSpaceMetr M st A = cl_Ball(z,r) holds A is closed
proof
  let A be Subset of TopSpaceMetr M;
  assume A = cl_Ball(z,r);
  then A` is open by Lm1;
  hence thesis by TOPS_1:3;
end;
