The Pytkeev property and the Reznichenko property in function spaces

For a Tychonoff space $X$ we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence. Characterizations of sequentiality and countable tightness of $C_p(X)$ in terms of $X$ were given by Gerlits, Nagy, Pytkeev and Arhangel'skii. In this paper, we characterize the Pytkeev property and the Reznichenko property of $C_p(X)$ in terms of $X$. In particular we note that if $C_p(X)$ over a subset $X$ of the real line is a Pytkeev space, then $X$ is perfectly meager and has universal measure zero