Eberly College of Arts and Sciences
We show that there exists a derivative f : [0, 1] → [0, 1] such that the graph of f ◦ f is dense in [0, 1]2 , so not a Gδ-set. In particular, f ◦ f is everywhere discontinuous, so not of Baire class 1, and hence it is not a derivative.
Digital Commons Citation
Ciesielski, Krzysztof, "On the Composition of Derivatives" (2018). Faculty & Staff Scholarship. 851.