reserve T,T1,T2,S for non empty TopSpace;
reserve GY for non empty TopSpace,
  r,s for Real;

theorem
  for G being non empty TopSpace, w1,w2,w3 being Point of G, 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;
