Lineability and spaceability of sets of functions on R

By R. Aron, Vladimir I. Gurariy, J. B. Seoane. 2004

312 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f861a5283f0f43dad819c218ce2a7f60678ac4ad

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Algebras in sets of queer functions (2007, unknown): “…that these sets of pathological functions are large in an algebraic sense: they contain a linear subspace (of large dimension), which is sometimes dense or closed, except, of course, for the zero function : see for instance [2] [5] [6] [9] [10] [12] [13] [15] [19], and [1] for a first survey.”
Algebraic genericity of strict-order integrability (2010, background): “In this respect, let us recall some recent terminology introduced in [1], [3], [5] and [8].”
Operator ranges and spaceability (2011, background): “The term ‘spaceable’ was introduced in [2] (see also [15]).”
Some results and open questions on spaceability in function spaces (2013, background): “These notions of lineability and spaceability were originally coined by Gurariy and they first appeared in [3, 29].”
Strong algebrability of sets of sequences and functions (2012, background): “In addition to algebrability, there exist other related properties such as lineability, dense-lineability and spaceability; see [3], [8], [9] and [14].”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “2 (Aron, Gurariy, and Seoane-Sepúlveda, 2005 [22]).”
Algebrability of the set of non-convergent Fourier series (2006, background): “We believe that the terms lineable and spaceable were first introduced in [5] and, later, in [2] and [7] (see also [1]).”
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]).”
Infinite dimensional Banach spaces of functions with nonlinear properties (2010, unknown): “Other pathological properties have been studied by various authors, for instance differentiable nowhere monotone functions and everywhere surjective functions in [3].”
Sierpinski-Zygmund functions and other problems on lineability (2010, methodology): “(See [4]: a function f : R → R is said to be everywhere surjective if f(I) = R for every non-trivial interval I.”
Lineability criteria, with applications (2013, background): “To this respect, let us recall some recent terminology introduced in [7], [12], [24] and [61].”