On Peano mappings (Q1307436)
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scientific article; zbMATH DE number 1355165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Peano mappings |
scientific article; zbMATH DE number 1355165 |
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On Peano mappings (English)
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31 October 1999
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The author gives a short proof of the following theorem of \textit{H. Hahn} [Ann. Mat. (3) 21, 33-55 (1913; JFM 44.0560.02)]: If \({\mathbf I}\) is a closed interval, and if \(\varphi:{{\mathbf I}}\to{\mathbf I}^2\) is continuous and onto, then \(\{y\in {\mathbf I}^2: \text{card} \varphi^{-1}(y)\geq 3\}\) is dense in \({\mathbf I}^2\).
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Peano mapping
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fiber cardinality
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JFM 44.0560.02
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