On the theorem converse to Jordan's curve theorem (Q2722119)
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scientific article; zbMATH DE number 1617367
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the theorem converse to Jordan's curve theorem |
scientific article; zbMATH DE number 1617367 |
Statements
11 July 2001
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Jordan curve
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\(d\)-set
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accessible point
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On the theorem converse to Jordan's curve theorem (English)
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The theorem mentioned in the title says that if a compact set \(K\) has two complementary domains in \(\mathbb R^2\), from each of which it is accessible at every point, then \(K\) is a simply closed curve. The author proves more general results weakening the accessibility assumption.
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