
theorem
  for S being non empty TopSpace, T being non empty pathwise_connected
TopSpace, s being Point of S, t being Point of T st S,T are_homeomorphic holds
  pi_1(S,s),pi_1(T,t) are_isomorphic
proof
  let S be non empty TopSpace;
  let T be non empty pathwise_connected TopSpace;
  let s be Point of S;
  let t be Point of T;
  given f being Function of S,T such that
A1: f is being_homeomorphism;
  reconsider f as continuous Function of S,T by A1;
  take pi_1-iso(the Path of t,f.s) * FundGrIso(f,s);
  FundGrIso(f,s) is bijective by A1,Th31;
  hence thesis by GROUP_6:64;
end;
