Open Access
2016 Accumulation Points of Graphs of Baire-1 and Baire-2 Functions
Balázs Maga
Real Anal. Exchange 41(2): 315-330 (2016).


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.


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Balázs Maga. "Accumulation Points of Graphs of Baire-1 and Baire-2 Functions." Real Anal. Exchange 41 (2) 315 - 330, 2016.


Published: 2016
First available in Project Euclid: 30 March 2017

zbMATH: 06848932
MathSciNet: MR3597323

Primary: 26A21
Secondary: 26A15

Keywords: accumulation points , Baire-1 functions , Baire-2 functions

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 2 • 2016
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