
theorem
  for T being non empty T_2 compact TopSpace, A,B being closed Subset of
  T st A misses B ex F being Function of T,R^1 st F is continuous & for x being
  Point of T holds 0 <= F.x & F.x <= 1 & (x in A implies F.x = 0) & (x in B
  implies F.x = 1) by Th20;
