A Jordan–Brouwer Separation Theorem for Polyhedral Pseudomanifolds
The Jordan Curve Theorem referring to a simple closed curve in the plane has a particularly simple proof in the case that the curve is polygonal, called the “raindrop proof”. We generalize the notion of a simple closed polygon to that of a polyhedral ( d −1)-pseudomanifold ( d ≥2) and prove a Jordan...
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| Veröffentlicht in: | Discrete & computational geometry 2009-09, Vol.42 (2), p.277-304 |
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| container_title | Discrete & computational geometry |
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| creator | Perles, Micha A. Martini, Horst Kupitz, Yaakov S. |
| description | The Jordan Curve Theorem referring to a simple closed curve in the plane has a particularly simple proof in the case that the curve is polygonal, called the “raindrop proof”. We generalize the notion of a simple closed polygon to that of a polyhedral (
d
−1)-pseudomanifold (
d
≥2) and prove a Jordan–Brouwer Separation Theorem for such a manifold embedded in ℝ
d
. As a by-product, we get bounds on the polygonal diameter of the interior and exterior of such a manifold which are almost tight. This puts the result within the frame of computational geometry. |
| doi_str_mv | 10.1007/s00454-009-9192-0 |
| format | Article |
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d
−1)-pseudomanifold (
d
≥2) and prove a Jordan–Brouwer Separation Theorem for such a manifold embedded in ℝ
d
. As a by-product, we get bounds on the polygonal diameter of the interior and exterior of such a manifold which are almost tight. This puts the result within the frame of computational geometry.</description><identifier>ISSN: 0179-5376</identifier><identifier>EISSN: 1432-0444</identifier><identifier>DOI: 10.1007/s00454-009-9192-0</identifier><identifier>CODEN: DCGEER</identifier><language>eng</language><publisher>New York: Springer-Verlag</publisher><subject>Combinatorics ; Computational Mathematics and Numerical Analysis ; Geometry ; Mathematics ; Mathematics and Statistics ; Polygons ; Theorems ; Topological manifolds</subject><ispartof>Discrete & computational geometry, 2009-09, Vol.42 (2), p.277-304</ispartof><rights>Springer Science+Business Media, LLC 2009</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c390t-bc061d8ffbcba0dd2a34d48f4fa0d819c638cf4a298f0b8428cda2f5b74a82993</citedby><cites>FETCH-LOGICAL-c390t-bc061d8ffbcba0dd2a34d48f4fa0d819c638cf4a298f0b8428cda2f5b74a82993</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00454-009-9192-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00454-009-9192-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Perles, Micha A.</creatorcontrib><creatorcontrib>Martini, Horst</creatorcontrib><creatorcontrib>Kupitz, Yaakov S.</creatorcontrib><title>A Jordan–Brouwer Separation Theorem for Polyhedral Pseudomanifolds</title><title>Discrete & computational geometry</title><addtitle>Discrete Comput Geom</addtitle><description>The Jordan Curve Theorem referring to a simple closed curve in the plane has a particularly simple proof in the case that the curve is polygonal, called the “raindrop proof”. We generalize the notion of a simple closed polygon to that of a polyhedral (
d
−1)-pseudomanifold (
d
≥2) and prove a Jordan–Brouwer Separation Theorem for such a manifold embedded in ℝ
d
. As a by-product, we get bounds on the polygonal diameter of the interior and exterior of such a manifold which are almost tight. 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d
−1)-pseudomanifold (
d
≥2) and prove a Jordan–Brouwer Separation Theorem for such a manifold embedded in ℝ
d
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| ispartof | Discrete & computational geometry, 2009-09, Vol.42 (2), p.277-304 |
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| subjects | Combinatorics Computational Mathematics and Numerical Analysis Geometry Mathematics Mathematics and Statistics Polygons Theorems Topological manifolds |
| title | A Jordan–Brouwer Separation Theorem for Polyhedral Pseudomanifolds |
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