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Albuquerque, N. and BernalGonzález, L. and Pellegrino, D. and SeoaneSepúlveda, Juan B. (2014) Peano curves on topological vector spaces. Linear algebra and its applications, 460 . pp. 8196. ISSN 00243795

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

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