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

theorem Th7:
  T is second-countable implies T is separable
proof
  assume T is second-countable;
  then
A1: weight T c= omega by WAYBEL23:def 6;
  density T c= weight T by Th5;
  then density T c= omega by A1;
  hence thesis by TOPGEN_1:def 13;
end;
