On very non-linear subsets on continuous functions



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Botelho, G. and Cariello, D. and Favaro, V.V. and Pellegrino, D. and Seoane-Sepúlveda, Juan B. (2014) On very non-linear subsets on continuous functions. Quarterly journal of mathematics, 65 (3). pp. 841-850. ISSN 0033-5606

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Official URL: http://qjmath.oxfordjournals.org/content/65/3/841.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.

Item Type:Article
Uncontrolled Keywords:lineability, continuous function, very non-linear set.
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:28237
Deposited On:10 Feb 2015 09:30
Last Modified:28 Nov 2016 08:11

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