A two-point set must be zero-dimensional
Author:
Abstract
We prove that any subset of R 2 {\mathbb {R}^2} that intersects no line in more than two points either is zero-dimensional or contains an arc. This is used to prove that any subset of R 2 {\mathbb {R}^2} that intersects each line in exactly two points is zero-dimensional, answering a question of Mauldin.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
http://www.ams.org/proc/1992-116-02/S0002-9939-1992-1093599-1/S0002-9939-1992-1093599-1.pdf
Reference3 articles.
1. Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51];Engelking, Ryszard,1977
2. S. Mazurkiewicz, Sur un ensemble plan qui a avec chaque droite deux et seulement deux points communs, C. R. Varsovie 7 (1914), 382-384.
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