theorem :: TMAP_1:132

for X, Y being non empty TopSpace
for X1, X2 being non empty SubSpace of X st X1 meets X2 holds
for f1 being continuous Function of X1,Y
for f2 being continuous Function of X2,Y st f1 | (X1 meet X2) = f2 | (X1 meet X2) & X1,X2 are_weakly_separated holds
f1 union f2 is continuous Function of (X1 union X2),Y