On a conjecture of Fink and Wood (Q1039858)
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scientific article; zbMATH DE number 5637107
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a conjecture of Fink and Wood |
scientific article; zbMATH DE number 5637107 |
Statements
On a conjecture of Fink and Wood (English)
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23 November 2009
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The author considers the so-called \(\mathcal O\)-convexity, see the paper [J. Geom. 62, No.~1--2, 99--120 (1998; Zbl 0923.52001)] by \textit{E. Fink} and \textit{D. Wood}, who asked if arbitrary connected \(\mathcal O\)-half-space is contractible provided the orientation set \(\mathcal O\) has the point-intersection property. The present note shows that this is true in every two-dimensional space but not true in some three-dimensional spaces.
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generalized convexity
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restricted-orientation convexity
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contractibility
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half-space
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simple connectivity
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