Israel Journal of Mathematics

, Volume 137, Issue 1, pp 321–354 | Cite as

On the structure ofn-point sets

  • Khalid Bouhjar
  • Jan J. Dijkstra


Letn be an integer greater than one. Our main result, called the “Structure Theorem” is that a set that containsn−1 disjoint continua that are cut by a single line cannot be ann-point set, that is, a set that meets every line in preciselyn points. This theorem unifies and significantly improves upon a number of known theorems. The second part of the paper is devoted to several theorems that address the question when a set that meets every line in at mostn points can be extended to ann-point set. These theorems also highlight the sharpness of the Structure Theorem.


Structure Theorem London Mathematical Society Dense Open Subset Nonempty Open Subset Countable Dense Subset 
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Copyright information

© Hebrew University 2003

Authors and Affiliations

  • Khalid Bouhjar
    • 1
  • Jan J. Dijkstra
    • 2
  1. 1.Afdeling WiskundeVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Afdeling WiskundeVrije UniversiteitAmsterdamThe Netherlands

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