reserve T,T1,T2,S for non empty TopSpace;

theorem Th3:
  for T be non empty TopSpace, a be Point of T ex f be Function of
  I[01], T st f is continuous & f.0 = a & f.1 = a
proof
  let T be non empty TopSpace, a be Point of T;
  take I[01] --> a;
  thus thesis by BORSUK_1:def 14,def 15,FUNCOP_1:7;
end;
