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2020 Characterizing the Coordinate Functions of Space Filling Curves
James Foran, Judit Kardos
Real Anal. Exchange 45(2): 411-424 (2020). DOI: 10.14321/realanalexch.45.2.0411

Abstract

The coordinate functions, \(f\) and \(g\), of a space filling curve are continuous functions from \([0,1]\) to \([0,1]\) so that \(F(t)=(f(t),g(t))\) maps \([0,1]\) onto the unit square. In the paper Coordinate Functions of Space Filling Curves written by Foran, several necessary conditions for a continuous function \(f\) are given for there to be a continuous \(g\) so that \(F(t)=(f(t),g(t))\) maps \([0,1]\) onto \([0,1]^2\). In this paper, we define a new condition for \(f\) that is both necessary and sufficient to assure that \(f\) has a matching coordinate function \(g\) such that \(F(t)=(f(t),g(t))\) fills the square.

Citation

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James Foran. Judit Kardos. "Characterizing the Coordinate Functions of Space Filling Curves." Real Anal. Exchange 45 (2) 411 - 424, 2020. https://doi.org/10.14321/realanalexch.45.2.0411

Information

Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07229055
MathSciNet: MR1887867
Digital Object Identifier: 10.14321/realanalexch.45.2.0411

Subjects:
Primary: 26A27

Keywords: coordinate function , Fubini theorem , Lebesgue curve , space filling curve

Rights: Copyright © 2020 Michigan State University Press

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Vol.45 • No. 2 • 2020
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