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;
reserve X1, X2 for non empty SubSpace of X;

theorem
  for X being non empty TopSpace holds (ex X0 being non empty SubSpace
  of X st X0 is dense proper) implies X is non discrete;
