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 nowhere_dense implies A is not dense
proof
  assume
A1: Int Cl A = {};
  assume A is dense;
  then Cl A = [#]X;
  hence contradiction by A1,TOPS_1:15;
end;
