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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebrability, non-linear properties, and special functions


Authors: Artur Bartoszewicz, Szymon Głab, Daniel Pellegrino and Juan B. Seoane-Sepúlveda
Journal: Proc. Amer. Math. Soc. 141 (2013), 3391-3402
MSC (2010): Primary 15A03; Secondary 28A20, 46J10
Published electronically: June 19, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct uncountably generated algebras inside the following sets of special functions: (i) Sierpiński-Zygmund functions, (ii) perfectly
everywhere surjective functions, (iii) nowhere continuous Darboux functions. All conclusions obtained in this paper are improvements of some already known results.


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Additional Information

Artur Bartoszewicz
Affiliation: Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland
Email: arturbar@p.lodz.pl

Szymon Głab
Affiliation: Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland
Email: szymon.glab@p.lodz.pl

Daniel Pellegrino
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900 - João Pessoa, Brazil
Email: pellegrino@pq.cnpq.br

Juan B. Seoane-Sepúlveda
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain
Email: jseoane@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11641-2
PII: S 0002-9939(2013)11641-2
Keywords: Lineability, spaceability, algebrability, perfectly everywhere surjective functions, Sierpi\'nski-Zygmund functions
Received by editor(s): September 16, 2011
Received by editor(s) in revised form: December 20, 2011
Published electronically: June 19, 2013
Additional Notes: The first and second authors were supported by the Polish Ministry of Science and Higher Education Grant No. N N201 414939 (2010-2013).
The fourth author was supported by the Spanish Ministry of Science and Innovation, Grant MTM2009-07848.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society