Baire category and nowhere differentiability for feasible real functions | Zendy

Breutzmann Josef M. | Zendy; Juedes David W. | Zendy; Lutz Jack H. | Zendy

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Baire category and nowhere differentiability for feasible real functions

Author(s) -

Breutzmann Josef M.,

Juedes David W.,

Lutz Jack H.

Publication year - 2004

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200310112

Subject(s) - mathematics , baire space , differentiable function , baire category theorem , bounded function , unit interval , class (philosophy) , baire measure , banach space , discrete mathematics , extension (predicate logic) , pure mathematics , mathematical analysis , artificial intelligence , computer science , programming language

A notion of resource‐bounded Baire category is developed for the class P C [0,1] of all polynomial‐time computable real‐valued functions on the unit interval. The meager subsets of P C [0,1] are characterized in terms of resource‐bounded Banach‐Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function in P C [0,1] is nowhere differentiable. This is a complexity‐theoretic extension of the analogous classical result that Banach proved for the class C [0, 1] in 1931. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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