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On very non-linear subsets of continuous functions

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Botelho, G. and Cariello, Daniel and Pellegrino, D. and Seoane-Sepúlveda, Juan B. (2014) On very non-linear subsets of 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


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http://arxiv.org/abs/1212.4395UNSPECIFIED


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 > Mathematical analysis
ID Code:29171
Deposited On:11 Mar 2015 09:41
Last Modified:28 Nov 2016 08:22

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