Israel Journal of Mathematics

, Volume 137, Issue 1, pp 321–354

On the structure ofn-point sets

• Khalid Bouhjar
• Jan J. Dijkstra
Article

Abstract

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.

Keywords

Structure Theorem London Mathematical Society Dense Open Subset Nonempty Open Subset Countable Dense Subset
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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