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;
reserve X for non empty TopSpace;

theorem
  for X1,X2 being non empty SubSpace of X st X1,X2
constitute_a_decomposition holds X1 is nowhere_dense iff X2 is everywhere_dense
  by Th37;
