
theorem Th19:
  for T being non empty normal TopSpace, A,B being closed Subset
  of T st A <> {} & A misses B holds 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)
proof
  let T be non empty normal TopSpace;
  let A,B be closed Subset of T;
  assume
A1: A <> {} & A misses B;
  set R = the Rain of A,B;
  take Thunder(R);
  thus thesis by A1,Th18;
end;
