Publication:
On very non-linear subsets on continuous functions

Thumbnail Image
Files
Seoane103.pdf (149.49 KB)
Official URL
http://qjmath.oxfordjournals.org/content/65/3/841.abstract
Full text at PDC
Publication Date
2014-09
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Oxford University Press
Citations
Google Scholar
Exportar
DC QDC MarcXML RDF MODS METS ORE-ATOM
Research Projects
Organizational Units
Journal Issue
Abstract
In this paper, we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for functions defined on certain subsets of R are actually true for functions on quite general topological spaces. In the line of the original results of Gurariy and Quarta, we prove that, depending on the desired dimension, such subspaces may exist or not.
Description
UCM subjects
AnĂĄlisis funcional y teorĂ­a de operadores
Unesco subjects
Keywords
Citation
[1] R.M. Aron, V.I. Gurariy, and J.B. Seoane-Sepullveda, lineability and spaceability of sets of functions on R. Proc. Amer. Math. Soc. 133 (2005) 795–803. [2] J. Dugundji, Topology, Allyn and Bacon Inc., Boston, Mass., 1966. [3] V.I. Gurariy and L. Quarta, On the lineability of sets of continuous functions, J. Math. Anal.Appl. 294 (2004), 62–72.
URI
https://hdl.handle.net/20.500.14352/33770
Collections
ArtĂ­culos