let X, Y be non empty TopSpace; :: thesis: for X1, X2 being non empty closed SubSpace of X
for g being Function of (X1 union X2),Y holds
( g is continuous Function of (X1 union X2),Y iff ( g | X1 is continuous Function of X1,Y & g | X2 is continuous Function of X2,Y ) )
let X1, X2 be non empty closed SubSpace of X; :: thesis: for g being Function of (X1 union X2),Y holds
( g is continuous Function of (X1 union X2),Y iff ( g | X1 is continuous Function of X1,Y & g | X2 is continuous Function of X2,Y ) )
let g be Function of (X1 union X2),Y; :: thesis: ( g is continuous Function of (X1 union X2),Y iff ( g | X1 is continuous Function of X1,Y & g | X2 is continuous Function of X2,Y ) )
X1,X2 are_weakly_separated by TSEP_1:80;
hence ( g is continuous Function of (X1 union X2),Y iff ( g | X1 is continuous Function of X1,Y & g | X2 is continuous Function of X2,Y ) ) by Th114; :: thesis: verum