n-point sets and graphs of functions

被引：2

作者：

Cobb, John ^{[1
]}

机构：

[1] Univ Idaho, Dept Math, Moscow, ID 83844 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2008年 / 155卷 / 16期

关键词：

n-point set; planar set; graph of a function;

D O I：

10.1016/j.topol.2008.05.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that, for every n >= 2, there exists an n-point set (a plane set which hits every line in exactly n points) that is homeomorphic to the graph of a function from R to R: for n >= 4, there exist both 0-dimensional and 1-dimensional examples. This raises the question (which we do not answer) of whether n-point sets for different n's could be homeomorphic. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1804 / 1807

页数：4

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