Open Access
2016 On Scottish Book Problem 157
Kevin Beanland, Paul D. Humke, Trevor Richards
Author Affiliations +
Real Anal. Exchange 41(2): 331-346 (2016).


This paper descibes our hunt for the solver of Problem 157 in the Scottish Book, a problem originally posed by A. J. (Gus) Ward in 1937. We first make the observation that a theorem of Richard O’Malley from 1975 yields an immediate positive solution. A further look at O’Malley’s references revealed a 1970 paper by Donald Ornstein that we now believe contains the first solution of SB 157. We isolate the common elements in the machinery used by both Ornstein and O’Malley and discuss several consequences. We also examine an example function given by Ornstein. There are some difficulties with this function but we provide a fix, and show moreover that functions of that kind are typical in the sense of the Baire category theorem.


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Kevin Beanland. Paul D. Humke. Trevor Richards. "On Scottish Book Problem 157." Real Anal. Exchange 41 (2) 331 - 346, 2016.


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

zbMATH: 1384.26021
MathSciNet: MR3597324

Primary: 26A24
Secondary: 26A48

Keywords: 157 , approximate continuity , approximate derivate , monotone , Scottish book

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 2 • 2016
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