The Pytkeev property and the Reznichenko property in function spaces

Abstract

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