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 Th26:
  B is nowhere_dense & A c= B implies A is nowhere_dense
proof
  assume B is nowhere_dense;
  then
A1: Cl B is boundary;
  assume A c= B;
  then Cl A is boundary by A1,Th11,PRE_TOPC:19;
  hence thesis;
end;
