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

L. Bernal-González; M. C. Calderón-Moreno; J. A. Prado-Bassas

doi:10.1016/j.laa.2014.11.014

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arXiv · 1407.3951

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

L. Bernal-González·M. C. Calderón-Moreno·J. A. Prado-Bassas

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Abstract

In this paper, a study of topological and algebraic properties of two families of functions from the unit interval $I$ into the plane $\mathbb{R}^2$ 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 $I \to \mathbb{R}^2$ 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.

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BibTeX RIS

L. Bernal-González, M. C. Calderón-Moreno, J. A. Prado-Bassas. 2014-07-15. The set of space-filling curves: topological and algebraic structure. https://doi.org/10.1016/j.laa.2014.11.014

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