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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 {f∘h: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...
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