let S, T be non empty TopSpace; :: thesis: ( S,T are_homeomorphic & S is simply_connected implies T is simply_connected )
assume ( S,T are_homeomorphic & S is simply_connected ) ; :: thesis: T is simply_connected
hence ( T is having_trivial_Fundamental_Group & T is pathwise_connected ) by Th13, TOPALG_3:9; :: according to TOPALG_6:def 2 :: thesis: verum