
theorem Th27:
  for S being Hausdorff TopLattice, x being Element of S st for a
  being Element of S holds a"/\" is continuous holds uparrow x is closed
proof
  let S be Hausdorff TopLattice, x be Element of S;
  assume for a being Element of S holds a"/\" is continuous;
  then
A1: x"/\" is continuous;
  (x"/\")"{x} = uparrow x & {x} is closed by Th7,PCOMPS_1:7;
  hence thesis by A1;
end;
