On the structure of n-point sets

K. Bouhjar, J.J. Dijkstra

Research output: Contribution to JournalArticleAcademicpeer-review

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. © 2003 Hebrew University.
Original languageEnglish
Pages (from-to)321-354
JournalIsrael Journal of Mathematics
Volume137
DOIs
Publication statusPublished - 2003

Bibliographical note

MR2013361

Fingerprint

Dive into the research topics of 'On the structure of n-point sets'. Together they form a unique fingerprint.

Cite this