Eberly College of Arts and Sciences
In this note we describe closed subsets of the real line P ⊂ R for which there exists a continuous function from P onto P 2 , called 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 R 2 admitting Peano functions, expressed in terms of connectedness and local connectedness.
Digital Commons Citation
Ciesielski, Krzysztof, "On Closed Subsets of ℝ and of ℝ2 Admitting Peano Functions" (2015). Faculty & Staff Scholarship. 849.