We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
ON VERY NON-LINEAR SUBSETS OF CONTINUOUS FUNCTIONS.
- Authors
Botelho, G.; Cariello, D.; Fávaro, V. V.; Pellegrino, D.; Seoane-Sepúlveda, J. B.
- 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.
- Subjects
VECTOR spaces; CONTINUOUS functions; TOPOLOGICAL spaces; CARDINAL numbers; AUTOMORPHISMS; LINEAR algebra
- Publication
Quarterly Journal of Mathematics, 2014, Vol 65, Issue 3, p841
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hat043