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), 795803
MSC (2000):
Primary 26A27, 46E10, 46E15
Published electronically:
August 24, 2004
MathSciNet review:
2113929
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We show that there is an infinitedimensional vector space of differentiable functions on every nonzero element of which is nowhere monotone. We also show that there is a vector space of dimension of functions every nonzero element of which is everywhere surjective.
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 P. Enflo, V. I Gurariy, On lineability and spaceability of sets in function spaces, to appear.
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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:
http://dx.doi.org/10.1090/S0002993904075331
PII:
S 00029939(04)075331
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 FQM257.
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2004
American Mathematical Society
