  Answering a question of Sakai, we show that the minimal cardinality of a set
of reals X such that C_p(X) does not have the Pytkeev property is equal to the
pseudo-intersection number p. Our approach leads to a natural characterization
of the Pytkeev property of C_p(X) by means of a covering property of X, and to
a similar result for the Reznicenko property of C_p(X).
