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Peano curves on topological vector spaces

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Albuquerque, N. y Bernal-González, L. y Pellegrino, D. y Seoane-Sepúlveda, Juan B. (2014) Peano curves on topological vector spaces. Linear algebra and its applications, 460 . pp. 81-96. ISSN 0024-3795

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0024379514004790


URLTipo de URL
http://arxiv.org/abs/1404.5876Institución


Resumen

The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from the real line R to any Euclidean space Rn. The algebraic structure of the set of these functions (as well as extensions to spaces with higher dimensions) is analyzed from the modern point of view of lineability, and large algebras are found within the families studied. We also investigate topological vector spaces that are continuous image of the real line, providing an optimal lineability result.


Tipo de documento:Artículo
Palabras clave:Peano curve; Peano space; Space-filling curve; Order of entire functions; Lineability; Spaceability
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:28232
Depositado:10 Feb 2015 09:26
Última Modificación:28 Nov 2016 08:25

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