Open Access
2018 On the Minkowski Sum of Two Curves
Andrew M. Bruckner, Krzysztof Chris Ciesielski
Real Anal. Exchange 43(1): 235-238 (2018). DOI: 10.14321/realanalexch.43.1.0235


We show that there exists a derivative \(f\colon [0,1]\to[0,1]\) such that the graph of \(f\circ f\) is dense in \([0,1]^2\), so not a \(G_\delta\)-set. In particular, \(f\circ f\) is everywhere discontinuous, so not of Baire class 1, and hence it is not a derivative. %neither of Baire class 1 nor a derivative.


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Andrew M. Bruckner. Krzysztof Chris Ciesielski. "On the Minkowski Sum of Two Curves." Real Anal. Exchange 43 (1) 235 - 238, 2018.


Published: 2018
First available in Project Euclid: 2 May 2018

MathSciNet: MR1377522
Digital Object Identifier: 10.14321/realanalexch.43.1.0235

Primary: 26A24
Secondary: 26A18

Keywords: composition , derivatives , fixed point

Rights: Copyright © 2018 Michigan State University Press

Vol.43 • No. 1 • 2018
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