let n be Nat; :: thesis:
let X be non empty TopSpace; :: thesis:
let f1, f2, g be Function of X,(TOP-REAL n); :: thesis:
assume that
A1: ( f1 is continuous & f2 is continuous ) and
A2: for p being Point of X holds g . p = (f1 . p) + (f2 . p) ; :: thesis:
consider h being Function of X,(TOP-REAL n) such that
A3: for r being Point of X holds h . r = (f1 . r) + (f2 . r) and
A4: h is continuous by A1, JGRAPH_6:12;
for x being Point of X holds g . x = h . x

let x be Point of X; :: thesis:
thus g . x = (f1 . x) + (f2 . x) by A2
.= h . x by A3 ; :: thesis:

end;