reserve T1,T2,T3 for TopSpace,
  A1 for Subset of T1, A2 for Subset of T2, A3 for Subset of T3;
reserve n,k for Nat;
reserve M,N for non empty TopSpace;
reserve p,q,p1,p2 for Point of TOP-REAL n;
reserve r for Real;

theorem
  for p,q being Point of TOP-REAL(n+1) st p<>0.TOP-REAL(n+1)
  holds TPlane(p,q) is n-manifold
proof
  let p,q be Point of TOP-REAL(n+1);
  assume p <> 0.TOP-REAL(n+1);
  then TOP-REAL n, TPlane(p,q) are_homeomorphic by Th29;
  hence thesis by Th12;
end;
