  We show that all finite powers of a Hausdorff space X do not contain
uncountable weakly separated subspaces iff there is a c.c.c poset P such that
1_P forces that ``X is a countable union of 0-dimensional subspaces of
countable weight.''
  We also show that this theorem is sharp in two different senses:
  (i) we can't get rid of using generic extensions,
  (ii) we have to consider all finite powers of $X$.
