On dense-lineability of sets of functions on R

By R. Aron, F. J. García-Pacheco, David Pérez-García, J. B. Seoane-Sep'ulveda. 2009

79 citations recorded by the source corpus.

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 ∪ { 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 C [ a , b ] . We also develop some techniques to show that the set of differentiable nowhere monotone functions is dense-lineable in C [ a , b ] . Other results related to density and dense-lineability of sets in Banach spaces are also presented.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80fefaf85703ad261c850c561229906607c781ac

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Sierpinski-Zygmund functions and other problems on lineability (2010, methodology): “In [4] it was proved that this set is א0-lineable using a different technique, and in [3] it has been shown that the set DNM([a, b]) is dense-lineable for any non-void interval [a, b].”
Lineability criteria, with applications (2013, methodology): “Then the class of functions f ∈ C [0, 1] such that f (p) is nowhere differentiable on [0, 1] is dense-lineable in C[0, 1] [6, 22].”
Algebraic genericity of strict-order integrability (2010, background): “[3] R. M. Aron, V. I. Gurariy and J. B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R, Proc.”
Spaceability in Banach and quasi-Banach sequence spaces (2010, background): “The last few years have witnessed the appearance of lots of papers concerning lineability and spaceability (see, for example, [1, 2, 3, 10, 13]).”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “More precisely, in [84] Bernal-González and Ordóñez-Cabrera provided a series of conditions on a measure space (Ω,Σ, μ) to ensure the spaceability of the sets Lp(Ω)\ ⋃ q∈[1,p) Lq(Ω), Lp(Ω)\ ⋃ q∈[p,∞) Lq(Ω), and Lp(Ω) \ ⋃ q∈[1,∞)\{p} Lq(μ,X) (for p ≥ 1); whereas in [111] Botelho, Fávaro, Pellegri”