  In this paper we provide solutions of the Harrington problem (along with a
few generalizations) proposed in a book Analytic Sets. The original problem
asks if for arbitrary sequence of continuous functions from \( \R^\omega \) to
a fixed compact interval we can find a subsequence point-wise convergent on
some product of perfect subsets of \( \R \). We reduce aforementioned problem
to functions from \( C^\omega \) to \(C\), where \(C\) is a standard Cantor set
as well as also provide solution to the problem with Baire functions in place
of continuous ones. Our main focus is on showing applications of the fusion
lemma - a result about perfect trees used among others to prove minimality of
Sack's forcing - to the problem at hand.
