for G being non empty TopSpace
for w1, w2, w3 being Point of G
for h1, h2 being Function of I[01],G st h1 is continuous & w1 = h1 . 0 & w2 = h1 . 1 & h2 is continuous & w2 = h2 . 0 & w3 = h2 . 1 holds
ex h3 being Function of I[01],G st
( h3 is continuous & w1 = h3 . 0 & w3 = h3 . 1 & rng h3 c= (rng h1) \/ (rng h2) ) by Lm3;