Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423389 | Discrete Mathematics | 2014 | 9 Pages |
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 {fâh: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 bÏ and we determine the minimal integer t=t(ε) that works for a given ε>0.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Stevo Todorcevic, Konstantinos Tyros,