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Planar compact sets whose intersections are starshaped via orthogonally convex paths
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Marilyn Breen
Veröffentlicht/Copyright:
21. Mai 2008
Abstract
A Helly-type theorem previously established for a finite family of simply connected orthogonal polygons may be extended to a family 
of planar compact sets having connected complements: If every three (not necessarily distinct) members of have a nonempty intersection that is starshaped via orthogonally convex paths, then all members of have such an intersection. When is finite, an analogous result holds with orthogonally convex paths replaced by staircase paths. The number three is best possible in each case. Moreover, the results fail without the requirement that the sets have connected complements.
Key words.: Sets starshaped via orthogonally convex paths
Received: 2006-10-25
Published Online: 2008-05-21
Published in Print: 2008-April
© de Gruyter 2008
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Artikel in diesem Heft
- A Kantor family admitting a normal F-factor constitutes a p-group
- Planar compact sets whose intersections are starshaped via orthogonally convex paths
- An improvement of a theorem of Van de Ven
- Quadratic modules of polynomials in two variables
- On arithmetic Zariski pairs in degree 6
- Ample vector bundles with zero loci of small Δ-genera
- Defect and Hodge numbers of hypersurfaces
- On rational maps from a general surface in to surfaces of general type
- Location of radial centres of convex bodies
Schlagwörter für diesen Artikel
Sets starshaped via orthogonally convex paths
Artikel in diesem Heft
- A Kantor family admitting a normal F-factor constitutes a p-group
- Planar compact sets whose intersections are starshaped via orthogonally convex paths
- An improvement of a theorem of Van de Ven
- Quadratic modules of polynomials in two variables
- On arithmetic Zariski pairs in degree 6
- Ample vector bundles with zero loci of small Δ-genera
- Defect and Hodge numbers of hypersurfaces
- On rational maps from a general surface in to surfaces of general type
- Location of radial centres of convex bodies
