Oscilation stability for continuous monotone surjections

Abstract

We prove that for every integer $b⩾2$ and positive real $\epsilon$ there exists a finite number $t$ such that for every finite coloring of the nondecreasing surjections from $b^{\omega }$ onto $b^{\omega }$, there exist $t$ many colors such that their $\epsilon$-fattening contains a cube.

12 pages