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Alternative Title
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. © The Author(s), 2020. Published by Cambridge University Press.
Keywords
03E02, 03E55, 05C55, 05D10, 54E40, MSC Codes
Source Title
Forum of Mathematics, Pi
Publisher
Cambridge University Press
Series/Report No.
Collections
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
Date
2020
DOI
10.1017/fmp.2020.12
Type
Article