let S, T, V be non empty TopSpace; :: thesis: ( S,T are_homeomorphic & T,V are_homeomorphic implies S,V are_homeomorphic )
assume that
A1: S,T are_homeomorphic and
A2: T,V are_homeomorphic ; :: thesis: S,V are_homeomorphic
consider f being Function of S,T such that
A3: f is being_homeomorphism by A1, T_0TOPSP:def 1;
consider g being Function of T,V such that
A4: g is being_homeomorphism by A2, T_0TOPSP:def 1;
g * f is being_homeomorphism by A3, A4, TOPS_2:57;
hence S,V are_homeomorphic by T_0TOPSP:def 1; :: thesis: verum