  Let M be the countably infinite metric fan. We show that C_k(M,2) is
sequential and contains a closed copy of Arens space S_2. It follows that if X
is metrizable but not locally compact, then C_k(X) contains a closed copy of
S_2, and hence does not have the property AP.
  We also show that, for any zero-dimensional Polish space X, C_k(X,2) is
sequential if and only if X is either locally compact or the derived set X' is
compact. In the case that X is a non-locally compact Polish space whose derived
set is compact, we show that all spaces C_k(X, 2) are homeomorphic, having the
topology determined by an increasing sequence of Cantor subspaces, the n-th one
nowhere dense in the (n+1)-st.
