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On dense-lineability of sets of functions on R

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Aron, R.M. and García-Pacheco, F.J. and Pérez García, David and Seoane-Sepúlveda, Juan B. (2009) On dense-lineability of sets of functions on R. Topology, 48 (2-4). pp. 149-156. ISSN 0040-9383

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Official URL: http://www.sciencedirect.com/science/article/pii/S0040938309000251


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Abstract

A subset M of a topological vector space X is said to be dense-lineable in X if there exists an infinite dimensional linear manifold in M boolean OR {0} and dense in X. We give sufficient conditions for a lineable set to be dense-lineable, and we apply them to prove the dense-lineability of several subsets of e[a, b]. We also develop some techniques to show that the set of differentiable nowhere monotone functions is dense-lineable in e[a, b]. Other results related to density and dense-lineability of sets in Banach spaces are also presented.


Item Type:Article
Uncontrolled Keywords:Dense-lineability; differentiable nowhere monotone functions
Subjects:Sciences > Mathematics > Functions
ID Code:17714
Deposited On:16 Jan 2013 11:32
Last Modified:28 Nov 2016 08:20

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