Knot points of typical continuous functions

David Preiss, Shingo Saito

Research output: Contribution to journalArticle


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 - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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