for T1, S1, T2, S2 being non empty TopSpace
for R1 being Refinement of T1,S1
for R2 being Refinement of T2,S2
for f being Function of T1,T2
for g being Function of S1,S2
for h being Function of R1,R2 st h = f & h = g & f is continuous & g is continuous holds
h is continuous