RT Journal Article
T1 Peano curves on topological vector spaces
A1 Albuquerque, N.
A1 Bernal-González, L.
A1 Pellegrino, D.
A1 Seoane Sepúlveda, Juan Benigno
AB 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.
PB Elsevier Science
SN 0024-3795
YR 2014
FD 2014-11-01
LK https://hdl.handle.net/20.500.14352/33768
UL https://hdl.handle.net/20.500.14352/33768
LA eng
NO PDSE/CAPES
NO Plan Andaluz de Investigacion de la Junta de Andalucia FQM-127 Grant
NO MEC
NO CNPq
DS Docta Complutense
RD 11 abr 2025