Oscilation stability for continuous monotone surjections

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

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