
theorem Th26:
  for S, T being non empty TopSpace, f being continuous Function
  of S,T, a being Point of S, P being Loop of a holds f*P is Loop of f.a
proof
  let S, T be non empty TopSpace;
  let f be continuous Function of S,T;
  let a be Point of S;
  let P be Loop of a;
A1: f.a,f.a are_connected;
A2: (f*P).1 = f.(P.j1) by FUNCT_2:15
    .= f.a by Th22;
  (f*P).0 = f.(P.j0) by FUNCT_2:15
    .= f.a by Th22;
  hence thesis by A2,A1,BORSUK_2:def 2;
end;
