let T be non empty TopSpace; :: thesis: ( T is second-countable implies T is separable )
assume T is second-countable ; :: thesis: T is separable
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 T is separable by TOPGEN_1:def 13; :: thesis: verum