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.