( [#] [:T1,T2:] <> {} & ( for P1 being Subset of [:T1,T2:] st P1 is open holds
[:f,g:] " P1 is open ) ) by Th9;
hence for b₁ being Function of [:S1,S2:],[:T1,T2:] st b₁ = [:f,g:] holds
b₁ is continuous by TOPS_2:43; :: thesis: verum