No 𝑛-point set is 𝜎-compact-Reference-Cited by-同舟云学术

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No 𝑛-point set is 𝜎-compact

Published:2000-09-27 Issue:2 Volume:129 Page:621-622
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bouhjar Khalid,Dijkstra Jan,Mauldin R.

Abstract

Let n n be an integer greater than 1. We prove that there exist no F σ F_\sigma -subsets of the plane that intersect every line in precisely n n points.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2001-129-02/S0002-9939-00-05869-X/S0002-9939-00-05869-X.pdf

Reference7 articles.

1. On a theorem of Larman;Baston, V. J.;J. London Math. Soc. (2),1972

2. K. Bouhjar, J. J. Dijkstra, and J. van Mill, Three-point sets, Topology Appl., to appear.

3. Die Grundlehren der mathematischen Wissenschaften, Band 153;Federer, Herbert,1969

4. A problem of incidence;Larman, D. G.;J. London Math. Soc.,1968

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1. On Some Coverings of the Euclidean Plane with Pairwise Congruent Circles;The American Mathematical Monthly;2010

2. There are no n-point Fσ sets in Rm;Bulletin of the Australian Mathematical Society;2005-12

3. On the structure ofn-point sets;Israel Journal of Mathematics;2003-12

4. Partial n-point sets and zero-dimensionality;Topology and its Applications;2003-02

5. ON SETS THAT MEET EVERY HYPERPLANE IN n-SPACE IN AT MOST n POINTS;Bulletin of the London Mathematical Society;2002-05

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