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On Closed Subsets Of ℝ And Of ℝ2 Admitting Peano Functions, Krzysztof Ciesielski
On Closed Subsets Of ℝ And Of ℝ2 Admitting Peano Functions, Krzysztof Ciesielski
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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.