Authors: Todorčević, Stevo 
Tyros, Konstantinos
Title: Oscillation stability for continuous monotone surjections
Journal: Discrete Mathematics
Volume: 324
Issue: 1
First page: 4
Last page: 12
Issue Date: 6-Jun-2014
Rank: M22
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.01.020
Abstract: 
We prove that for every real ε>0 there exists a positive integer t such that for every finite coloring of the nondecreasing surjections from [0,1] onto [0,1] there exist t many colors such that their ε-fattening contains a cube, i.e. a set of the form {fâ̂̃h:fnondecreasingsurjection from[0,1]onto[0,1]} where h is a nondecreasing surjection from [0,1] onto [0,1]. We prove this as a consequence of a corresponding result about bω and we determine the minimal integer t=t(ε) that works for a given ε>0.
Keywords: Cantor set | Dual Ramsey theory | Ramsey degree | Unit interval
Publisher: Elsevier

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