reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A, B for Subset of X;

theorem
  A is dense iff for C being Subset of X st A c= C & C is closed holds C
  = the carrier of X
by TOPS_1:5,PRE_TOPC:18;
