Between the Pytkeev and Frechet-Urysohn properties of function spaces

In this talk we aim to compare the Frechet-Urysohn property and some of its formal weakenings for spaces of the form C_p(X). In particular, we plan to present a sketch of the construction under CH of a set of reals X such that C_p(X) has the Pytkeev property (i.e., for every subset A of C_p(X) containing 0 in its closure, there exists a countable family {B_n: n\in w} of infinite subsets of A such that each neighbourhood of 0 contains some B_n), but fails to be Frechet-Urysohn. It is known that such spaces cannot be constructed outright in ZFC. The talk will be mainly based on a joint work in progress with S. Bardyla and J. Supina. The details of the Zoom meeting will be sent separately.