We solve the last standing open problem from the seminal paper by J. Gerlits and Zs. Nagy [Topology Appl. 14 (1982), pp. 151–161], which was later reposed by A. Miller, T. Orenshtein, and B. Tsaban. Namely, we show that under p = c \mathfrak {p}=\mathfrak {c} there is a δ \delta -set that is not a γ \gamma -set. Thus we constructed a subset A A of reals such that the space C p ( A ) \mathrm {C}_p(A) of all real-valued continuous functions on A A is not Fréchet–Urysohn, but possesses the Pytkeev property. Moreover, under C H \mathbf {CH} we construct a π \pi -set that is not a δ \delta -set solving a problem by M. Sakai. In fact, we construct various examples of δ \delta -sets that are not γ \gamma -sets, satisfying finer properties parametrized by ideals on natural numbers. Finally, we distinguish ideal variants of the Fréchet–Urysohn property for many different Borel ideals in the realm of functional spaces.