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