  We solve the last standing open problem from the seminal paper by J. Gerlits
and Zs. Nagy, which was later reposed by A. Miller, T. Orenshtein and B.
Tsaban. Namely, we show that under p = c there is a \delta-set that is not a
\gamma-set. Thus we construct a set of reals A such that the space Cp(A) of all
real-valued continuous functions on A is not Frechet-Urysohn, but possesses the
Pytkeev property. Moreover, under CH we construct a \pi-set that is not a
\delta-set solving a problem by M. Sakai. In fact, we construct various
examples of \delta-sets that are not \gamma-sets, satisfying finer properties
parametrized by ideals on natural numbers. Finally, we distinguish ideal
variants of the Frechet-Urysohn property for many different Borel ideals in the
realm of functional spaces.
