Artículo
Peano curves on topological vector spaces
Autor/es | Gurgel e Albuquerque, Nacib André
Bernal González, Luis Pellegrino, Daniel M. Seoane Sepúlveda, Juan Benigno |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2014-11-01 |
Fecha de depósito | 2016-07-01 |
Publicado en |
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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 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. |
Identificador del proyecto | FQM-127
P08-FQM-03543 info:eu-repo/grantAgreement/MINECO/MTM2012-34847-C02-01 401735/2013-3 |
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. |
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