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Peano curves on topological vector spaces

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Albuquerque, N. and Bernal-González, L. and Pellegrino, D. and 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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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379514004790


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http://arxiv.org/abs/1404.5876Organisation


Abstract

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.


Item Type:Article
Uncontrolled Keywords:Peano curve; Peano space; Space-filling curve; Order of entire functions; Lineability; Spaceability
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:28232
Deposited On:10 Feb 2015 09:26
Last Modified:28 Nov 2016 08:25

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