 reserve n,m for Nat,
         p,q for Point of TOP-REAL n, r for Real;
reserve M,M1,M2 for non empty TopSpace;

theorem
  M is without_boundary locally_euclidean non empty TopSpace
    iff
  for p be Point of M
    ex U be a_neighborhood of p,n st
      M|U,Tball(0.TOP-REAL n,1) are_homeomorphic by Lm2;
