Knot points of typical continuous functions

David Preiss, Shingo Saito

Research output: Contribution to journalArticlepeer-review


It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strongest possible sense except in a small set of points. In this paper, we completely characterise families S of sets of points for which most continuous functions have the property that such small set of points belongs to S. The proof uses a topological zero-one law and the Banach-Mazur game.

Original languageEnglish
Pages (from-to)833-856
Number of pages24
JournalTransactions of the American Mathematical Society
Issue number2
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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