reserve X for non empty TopSpace,
  A,B for Subset of X;
reserve Y1,Y2 for non empty SubSpace of X;
reserve X1, X2 for non empty SubSpace of X;

theorem
  for X1,X2 being non empty SubSpace of X st X1,X2
  constitute_a_decomposition holds X1 is boundary iff X2 is dense by Th31;
