theorem :: TOPALG_3:19

for S, T, T1, T2, Y being non empty TopSpace
for f being Function of [:Y,T1:],S
for g being Function of [:Y,T2:],S
for F1, F2 being closed Subset of T st T1 is SubSpace of T & T2 is SubSpace of T & F1 = [#] T1 & F2 = [#] T2 & ([#] T1) \/ ([#] T2) = [#] T & f is continuous & g is continuous & ( for p being set st p in ([#] [:Y,T1:]) /\ ([#] [:Y,T2:]) holds
f . p = g . p ) holds
ex h being Function of [:Y,T:],S st
( h = f +* g & h is continuous )