
theorem Th9:

:: 1.2. LEMMA (i), p. 143
  for S,T being lower complete TopLattice, f being Function of S, T
  st f is infs-preserving holds f is continuous
proof
  let S,T be lower complete non empty TopLattice;
  let f be Function of S,T;
  assume f is infs-preserving;
  then for X being non empty Subset of S holds f preserves_inf_of X;
  hence thesis by Th8;
end;
