Abstract
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.
Citation
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.