## Real Analysis Exchange

### On the Minkowski Sum of Two Curves

#### Abstract

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

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

Dates
First available in Project Euclid: 2 May 2018