@article{AppellBritoReinwand2022,
  author    = {Appell, J{\"u}rgen and Brito, Bel{\´e}n L{\´o}pez and Reinwand, Simon},
  title     = {Counterexamples on compositions},
  series = {Mathematische Semesterberichte},
  volume    = {70},
  journal   = {Mathematische Semesterberichte},
  number    = {1},
  issn      = {0720-728X},
  doi       = {10.1007/s00591-022-00318-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324306},
  pages     = {43-56},
  year      = {2022},
  abstract  = {We give a collection of 16 examples which show that compositions \(g\) \(\circ\) \(f\) of well-behaved functions \(f\) and \(g\) can be badly behaved. Remarkably, in 10 of the 16 examples it suffices to take as outer function \(g\) simply a power-type or characteristic function. Such a collection of examples may serve as a source of exercises for a calculus course.},
  language  = {en}
}