Real Analysis Exchange

On the Minkowski Sum of Two Curves

Andrew M. Bruckner and Krzysztof Chris Ciesielski

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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.

Article information

Real Anal. Exchange, Volume 43, Number 1 (2018), 235-238.

First available in Project Euclid: 2 May 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
Secondary: 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]

derivatives composition fixed point


Bruckner, Andrew M.; Ciesielski, Krzysztof Chris. On the Minkowski Sum of Two Curves. Real Anal. Exchange 43 (2018), no. 1, 235--238. doi:10.14321/realanalexch.43.1.0235.

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