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.
Primary Subjects: 28A05, 03E15
Secondary Subjects: 26A24
Keywords: Mazurkiewicz's theorem; $\pmb\Pi^1_1$--complete sets
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Permanent link to this document: http://projecteuclid.org/euclid.rae/1256835202
Real Analysis Exchange
