Linear subsets of nonlinear sets in topological vector spaces

By L. González, Daniel Pellegrino, J. Sepúlveda. 2013

234 citations recorded by the source corpus.

For the last decade there has been a generalized trend in mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special properties. This trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis, operator theory, summability theory, polynomials in Banach spaces, hypercyclicity and chaos, and general functional analysis. This expository paper is devoted to providing an account on the advances and on the state of the art of this trend, nowadays known as lineability and spaceability.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5fe13760eeee803a4b99e82746a6858c61eb64fc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. L. Bernal-Gonz'alez
2. Manuel Ord'onez-Cabrera

In Applied Mathematics

1. Manuel Ord'onez-Cabrera
2. L. Bernal-Gonz'alez
3. Alfredo Peris
4. J. Bes

In Mathematical Physics

1. Manuel Ord'onez-Cabrera
2. L. Bernal-Gonz'alez

Citations in the corpus

• Lineability criteria, with applications (2013, background): “ies offunctions ϕ: R→ Rthataresurjective in very strong senses (for instance, satisfying ϕ(I) = Rfor every interval I, and even with stronger conditions) have recently studied by several authors (see [7, 9, 31, 50, 51, 56]). However, all of these functions are nowhere continuous. It is then natural ”