Three-point sets

✍ Scribed by Khalid Bouhjar; Jan J. Dijkstra; Jan van Mill

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 161 KB
• Volume: 112
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00232-1

✦ Synopsis

We prove that a planar set which meets each line in exactly three points cannot contain a continuum and cannot be an F σ -set. We also present some results on extending and splitting n-point sets. Our results imply that there is a four-point set which contains an arc.