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2015 On Closed Subsets of $\mathbb{R}$ and of $\mathbb{R}^2$ Admitting Peano Functions
Krzysztof Chris Ciesielski, Jakub Jasinski
Real Anal. Exchange 40(2): 309-318 (2015).


In this note we describe closed subsets of the real line $P\subset {\mathbb R}$ for which there exists a continuous function from $P$ onto $P^2$, called a Peano function. Our characterization of those sets is based on the number of connected components of $P$. We also include a few remarks on compact subsets of $\mathbb{R}^2$ admitting Peano functions, expressed in terms of connectedness and local connectedness.


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Krzysztof Chris Ciesielski. Jakub Jasinski. "On Closed Subsets of $\mathbb{R}$ and of $\mathbb{R}^2$ Admitting Peano Functions." Real Anal. Exchange 40 (2) 309 - 318, 2015.


Published: 2015
First available in Project Euclid: 4 April 2017

zbMATH: 06848838
MathSciNet: MR3499767

Primary: 26A30
Secondary: 26B05

Keywords: Peano curve , space filling curve

Rights: Copyright © 2015 Michigan State University Press

Vol.40 • No. 2 • 2015
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