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

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 graph. 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 $f:[0,1]\to \mathbb{R}$ 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.

arXiv commentPublished in Real Analysis Exchange, Volume 41, Issue 2. Earlier available as "Accumulation Points of Graphs of Real Functions", apart from the title, the paper has not been modified

Cited by in corpus (1)

• Characterizations and Properties of Graphs of Baire Functions