2014/07/15 by L. Bernal-González, M. C. Calderón-Moreno, J. A. Prado-Bassas
Mathematics · #Advanced Banach Space Theory #Algebraic number #Algebraic structure #Combinatorics #Computer science #Holomorphic and Operator Theory #Mathematical analysis #Mathematics #Pure mathematics #Set (abstract data type) #Space (punctuation) #Topology (electrical circuits) #advanced mathematical theories #math.GN #msc:15A03 #msc:20M05 #msc:46E15 #msc:54E40 #msc:54F15
paper · pdf · doi:10.1016/j.laa.2014.11.014
published as Linear Algebra and its Applications, 467 (2015), 57-74
arxiv created 2014/07/15 · openalex publication_date 2014/11/19 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.