reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T,
  x for set;

theorem
  Fr {}T = {}
proof
  Fr {}T = Cl {}T /\ Cl ({}T)` by TOPS_1:def 2
    .= {} /\ Cl ({}T)`;
  hence thesis;
end;
