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

theorem Th46:
  for T being countable TopSpace holds T is separable
proof
  let T be countable TopSpace;
  card [#]T c= omega & density T c= card [#]T by Def12,CARD_3:def 14;
  then density T c= omega;
  hence thesis;
end;
