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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Knot points of typical continuous functions


Authors: David Preiss and Shingo Saito
Journal: Trans. Amer. Math. Soc. 366 (2014), 833-856
MSC (2010): Primary 26A27; Secondary 26A21, 28A05, 54H05
Published electronically: September 26, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: 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 $ \mathcal {S}$ of sets of points for which most continuous functions have the property that such small set of points belongs to $ \mathcal {S}$. The proof uses a topological zero-one law and the Banach-Mazur game.


References [Enhancements On Off] (What's this?)

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Additional Information

David Preiss
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: d.preiss@warwick.ac.uk

Shingo Saito
Affiliation: Institute of Mathematics for Industry, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
Address at time of publication: Faculty of Arts and Science, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
Email: ssaito@imi.kyushu-u.ac.jp, ssaito@artsci.kyushu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-06100-4
PII: S 0002-9947(2013)06100-4
Received by editor(s): April 13, 2012
Published electronically: September 26, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.