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During the last few decades E. S. Thomas, S. J. Agronsky, J. G. Ceder, and T.L. Pearson gave an equivalent definition of the real Baire class 1 functions bycharacterizing their graph. In this paper, using their results, we consider thefollowing problem: let $T$ be a given subset of $[0,1]\times\mathbb{R}$. Whencan we find a function $f:[0,1]\rightarrow\mathbb{R}$ such that theaccumulation points of its graph are exactly the points of $T$? We show that ifsuch a function exists, we can choose it to be a Baire-2 function. Wecharacterize the accumulation sets of bounded and not necessarily boundedfunctions separately. We also examine the similar question in the case ofBaire-1 functions.

Accumulation Points of Graphs of Baire-1 and Baire-2 Functions