let S1, S2, T1, T2 be non empty TopSpace; :: thesis: for f being continuous Function of S1,T1
for g being continuous Function of S2,T2 holds [:f,g:] is continuous
let f be continuous Function of S1,T1; :: thesis: for g being continuous Function of S2,T2 holds [:f,g:] is continuous
let g be continuous Function of S2,T2; :: thesis: [:f,g:] is continuous
( [#] [:T1,T2:] <> {} & ( for P1 being Subset of [:T1,T2:] st P1 is open holds
[:f,g:] " P1 is open ) ) by Th11;
hence [:f,g:] is continuous by TOPS_2:55; :: thesis: verum