On the Complexity of Continuous Functions Differentiable on Cocountable Sets
Szymon Głb
Source: Real Anal. Exchange Volume 34, Number 2
(2008), 521-530.
Abstract
We prove that the set of all functions in $C[0,1]$, with countably many points at which the derivative does not exist, is ${\pmb \Pi}^1_1$--complete, in particular non--Borel. We obtain the classical Mazurkiewicz's theorem and the recent result of Sofronidis as corollaries from our result.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1256835202
Mathematical Reviews number (MathSciNet): MR2569202
References
Becker, H., Some examples of Borel-inseparable pairs of coanalytic sets, Mathematika, 33(1) (1986), 72–79.
Mathematical Reviews (MathSciNet): MR859499
Digital Object Identifier: doi:10.1112/S0025579300013887
Kechris, A. S., On the concept of ${\pmb \Pi}\sp 1\sb 1$-completeness, Proc. Amer. Math. Soc., 125(6) (1997), 1811–1814.
Mathematical Reviews (MathSciNet): MR1372034
Zentralblatt MATH: 0864.03034
Digital Object Identifier: doi:10.1090/S0002-9939-97-03770-2
Kechris, A. S., Classical Descriptive Set Theory, (English summary) Graduate Texts in Mathematics, 156, Springer-Verlag, New York, 1995.
Mathematical Reviews (MathSciNet): MR1321597
Zentralblatt MATH: 0819.04002
Kuratowski, K., Topology, Vol. I, new edition, revised and augmented, translated from the French by J. Jaworowski, Academic Press, Państwowe Wydawnictwo Naukowe, New York-London, Warsaw, 1966.
Mathematical Reviews (MathSciNet): MR217751
Mauldin, R. D., The set of continuous nowhere differentiable functions, Pacific J. Math., 83(1) (1979), 199–205.
Mathematical Reviews (MathSciNet): MR555048
Project Euclid: euclid.pjm/1102784670
Sofronidis, N. E., The set of continuous piecewise differentiable functions, Real Anal. Exchange, 31(1) (2005–2006), 13–22.
Mathematical Reviews (MathSciNet): MR2218185
Zentralblatt MATH: 1094.03035
Project Euclid: euclid.rae/1149516810
Real Analysis Exchange
