theorem Th115:
  for X1, X2 being closed non empty 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
proof
  let X1, X2 be closed non empty SubSpace of X;
  let g be Function of X1 union X2,Y;
  X1,X2 are_weakly_separated by TSEP_1:80;
  hence thesis by Th114;
end;
