Preiss, David and Saito, Shingo (2014) Knot points of typical continuous functions. Transactions of the American Mathematical Society, Volume 366 (Number 2). pp. 833-856. doi:10.1090/S0002-9947-2013-06100-4 ISSN 0002-9947.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Knot theory, Functions, Continuous, Point set theory
Journal or Publication Title:	Transactions of the American Mathematical Society
Publisher:	American Mathematical Society
ISSN:	0002-9947
Official Date:	2014
Dates:	Date Event 2014 Published 26 September 2013 Available
Volume:	Volume 366
Number:	Number 2
Page Range:	pp. 833-856
DOI:	10.1090/S0002-9947-2013-06100-4
Status:	Peer Reviewed
Publication Status:	Published
Date of first compliant deposit:	26 December 2015
Date of first compliant Open Access:	26 December 2015

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