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The set of space-filling curves: topological and algebraic structure

Opened Access The set of space-filling curves: topological and algebraic structure

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Autor: Bernal González, Luis
Calderón Moreno, María del Carmen
Prado Bassas, José Antonio
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2015-02-15
Publicado en: Linear Algebra and its Applications, 467, 57-74.
Tipo de documento: Artículo
Resumen: In this paper, a study of topological and algebraic properties of two families of functions from the unit interval I into the plane R2 is performed. The first family is the collection of all Peano curves, that is, of those continuous mappings onto the unit square. The second one is the bigger set of all space-filling curves, i.e. of those continuous functions I → R2 whose images have positive Jordan content. Emphasis is put on the size of these families, in both topological and algebraic senses, when endowed with natural structures.
Cita: Bernal González, L., Calderón Moreno, M.d.C. y Prado Bassas, J.A. (2015). The set of space-filling curves: topological and algebraic structure. Linear Algebra and its Applications, 467, 57-74.
Tamaño: 218.2Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42893

DOI: 10.1016/j.laa.2014.11.014

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