## Real Analysis Exchange

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

Balázs Maga

#### Abstract

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 by characterizing their graphs. In this paper, using their results, we consider the following problem: let $T$ be a given subset of $[0,1]\times\mathbb{R}$. When can we find a function $f:[0,1]\rightarrow\mathbb{R}$ such that the accumulation points of its graph are exactly the points of $T$? We show that if such a function exists, we can choose it to be a Baire-2 function. We characterize the accumulation sets of bounded and not necessarily bounded functions separately. We also examine the similar question in the case of Baire-1 functions.

#### Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 315-330.

Dates
First available in Project Euclid: 30 March 2017