Families of planar sets having starlike union (Q1299934)
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scientific article; zbMATH DE number 1332737
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Families of planar sets having starlike union |
scientific article; zbMATH DE number 1332737 |
Statements
Families of planar sets having starlike union (English)
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7 September 1999
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A polygonal path consisting of \(k\) segments is called a \(k\)-path. The main result is as follows. Let \(F\) be a finite family of compact sets in the plane, and \(k\) be a fixed natural number. If every three members of \(F\) have a union which is simply connected and starshaped via \(k\)-paths, then all members of \(F\) have a common point and their union is starshaped via \(k\)-paths.
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Krasnosel'skii's theorem
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starshaped sets
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