Opened Access Peano curves on topological vector spaces

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Autor: Gurgel e Albuquerque, Nacib André
Bernal González, Luis
Pellegrino, Daniel M.
Seoane Sepúlveda, Juan Benigno
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-11-01
Publicado en: Linear Algebra and its Applications, 460, 81-96.
Tipo de documento: Artículo
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 R n . 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.
Cita: Gurgel e Albuquerque, N.A., Bernal González, L., Pellegrino, D.M. y Seoane Sepúlveda, J.B. (2014). Peano curves on topological vector spaces. Linear Algebra and its Applications, 460, 81-96.
Tamaño: 521.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43012

DOI: http://dx.doi.org/10.1016/j.laa.2014.07.029

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