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 Th33:
  A is everywhere_dense implies A is dense
proof
  assume A is everywhere_dense;
  then Cl Int A = [#] X;
  then [#]X c= Cl A by PRE_TOPC:19,TOPS_1:16;
  then Cl A = [#]X;
  hence thesis;
end;
