Lineability and spaceability of sets of functions on

Authors:
Richard Aron, V. I. Gurariy and J. B. Seoane

Journal:
Proc. Amer. Math. Soc. **133** (2005), 795-803

MSC (2000):
Primary 26A27, 46E10, 46E15

DOI:
https://doi.org/10.1090/S0002-9939-04-07533-1

Published electronically:
August 24, 2004

MathSciNet review:
2113929

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that there is an infinite-dimensional vector space of differentiable functions on every non-zero element of which is nowhere monotone. We also show that there is a vector space of dimension of functions every non-zero element of which is everywhere surjective.

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Additional Information

**Richard Aron**

Affiliation:
Department of Mathematics, Kent State University, Kent, Ohio 44242

Email:
aron@math.kent.edu

**V. I. Gurariy**

Affiliation:
Department of Mathematics, Kent State University, Kent, Ohio 44242

Email:
gurariy@math.kent.edu

**J. B. Seoane**

Affiliation:
Department of Mathematics, Kent State University, Kent, Ohio 44242

Email:
jseoane@math.kent.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07533-1

Received by editor(s):
March 26, 2003

Received by editor(s) in revised form:
October 28, 2003

Published electronically:
August 24, 2004

Additional Notes:
The author thanks Departamento de Matemáticas of the Universidad de Cádiz (Spain), especially Antonio Aizpuru, Fernando León, Javier Pérez, and the rest of the members of the group FQM-257.

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2004
American Mathematical Society