theorem :: TOPALG_3:20

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