Proof of a conjecture of Galvin

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2018-09-04 DOI:10.1017/fmp.2020.12

Dilip Raghavan, S. Todorcevic

引用次数: 7

Abstract

Abstract We prove that if the set of unordered pairs of real numbers is coloured by finitely many colours, there is a set of reals homeomorphic to the rationals whose pairs have at most two colours. Our proof uses large cardinals and verifies a conjecture of Galvin from the 1970s. We extend this result to an essentially optimal class of topological spaces in place of the reals.

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高尔文猜想的证明

摘要证明了如果实数的无序对集合被有限种颜色着色，则存在一组实数同胚于其对至多有两种颜色的有理数。我们的证明使用了大基数，并验证了20世纪70年代Galvin的一个猜想。我们将这个结果推广到一个本质上最优的拓扑空间类来代替实数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

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