reserve a, b, c, d, r, s for Real,
  n for Element of NAT,
  p, p1, p2 for Point of TOP-REAL 2,
  x, y for Point of TOP-REAL n,
  C for Simple_closed_curve,
  A, B, P for Subset of TOP-REAL 2,
  U, V for Subset of (TOP-REAL 2)|C`,
  D for compact with_the_max_arc Subset of TOP-REAL 2;

theorem Th70:
  for h being Homeomorphism of TOP-REAL 2 holds
  h.:C is being_simple_closed_curve
proof
  let h be Homeomorphism of T2;
  consider f being Function of T2|R^2-unit_square, T2|C such that
A1: f is being_homeomorphism by TOPREAL2:def 1;
  reconsider g = h|C as Function of T2|C,T2|(h.:C) by JORDAN24:12;
  take g*f;
  g is being_homeomorphism by JORDAN24:14;
  hence thesis by A1,TOPS_2:57;
end;
