theorem Th1: :: JGRAPH_2:1

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