Bulletin of the Belgian Mathematical Society - Simon Stevin

Large algebraic structures inside the set of surjective functions

José L. Gámez-Merino

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In this note we study large linear structures inside the set of Jones functions, which is a {\em highly pathological class} of surjective functions. We show that there exists an infinite dimensional linear space inside this set of functions. Moreover, we show that this linear space is isomorphic to \(\mathbb{R}^\mathbb{R}\), that is, it has the {\em biggest} possible dimension. The result presented in this note is an improvement of several recent results in the topic of {\em lineability}.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 2 (2011), 297-300.

First available in Project Euclid: 7 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A03: Vector spaces, linear dependence, rank 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

Lineability spaceability Jones functions


Gámez-Merino, José L. Large algebraic structures inside the set of surjective functions. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 2, 297--300. https://projecteuclid.org/euclid.bbms/1307452079

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