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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