theorem :: TMAP_1:119

for X, Y being non empty TopSpace
for f being Function of X,Y
for X1, X2 being non empty open SubSpace of X holds
( f | (X1 union X2) is continuous Function of (X1 union X2),Y iff ( f | X1 is continuous Function of X1,Y & f | X2 is continuous Function of X2,Y ) )