  Two natural questions are answered in the negative:
  (1) If a space has the property that small nulhomotopic loops bound small
nulhomotopies, then are loops which are limits of nulhomotopic loops themselves
nulhomotopic?
  (2) Can adding arcs to a space cause an essential curve to become
nulhomotopic?
  The answer to the first question clarifies the relationship between the
notions of a space being homotopically Hausdorff and $\pi_1$-shape injective.
