reserve a, r, s for Real;

theorem Th27:
  for S being being_simple_closed_curve SubSpace of TOP-REAL 2, x
  being Point of S holds INT.Group, pi_1(S,x) are_isomorphic
proof

set r = the positive Real,o = the Point of TOP-REAL 2,y = the Point of
Tcircle(o,r);
  let S be being_simple_closed_curve SubSpace of TOP-REAL 2, x be Point of S;
  INT.Group,pi_1(Tcircle(o,r),y) are_isomorphic & pi_1(Tcircle(o,r),y),
  pi_1(S,x) are_isomorphic by Lm16,TOPALG_3:33,TOPREALB:11;
  hence thesis by GROUP_6:67;
end;
