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Lineability and spaceability of sets of functions on 
Author(s):
Richard
Aron;
V.
I.
Gurariy;
J.
B.
Seoane
Journal:
Proc. Amer. Math. Soc.
133
(2005),
795-803.
MSC (2000):
Primary 26A27, 46E10, 46E15
Posted:
August 24, 2004
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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.
References:
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- 3.
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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:
10.1090/S0002-9939-04-07533-1
PII:
S 0002-9939(04)07533-1
Received by editor(s):
March 26, 2003
Received by editor(s) in revised form:
October 28, 2003
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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