A perplexing collection of Baire one functions (Q1852328)

The authors deal with functions \(f: [0,1]\to\mathbb{R}\). The paper is a continuation, in some sense, of the paper [\textit{M. J. Evans}, \textit{P. D. Humke} and \textit{R. J. O'Malley}, ``Universally polygonally approximable functions'', J. Appl. Anal. 6, No. 1, 25-45 (2000; Zbl 0965.26003)]. The class of universally polygonally approximable functions UPA and the closure of that class are investigated. The classes of interpolatively continuous functions IC and functions having the delta-fine property DF, are introduced. It is shown that \[ \text{B1}\cap \text{QC}\underset{\text{nwd}}\subset \text{UPA}\subset \text{DF} \underset{\text{nwd}}\subset \text{B1}\cap \text{IC} \underset{\text{nwd}}\subset \text{B1}, \] where QC (B1) is the class of all quasi-continuous (Baire 1) functions. The symbol \(\underset{\text{nwd}}\subset\) is to be read ``is a nowhere dense subset of'' where the sup metric is understood. The problem to give a descriptive characterization of either UPA or its closure remains open.