Exercise 8.5.7.11 (Composition of Dyadic Homeomorphisms). Let $s,t,u \geq 0$ be dyadic rational numbers and let $f: [0,s] \xrightarrow {\sim } [0,t]$ and $g: [0,t] \xrightarrow {\sim } [0,u]$ be dyadic homeomorphisms. Show that the composition $(g \circ f): [0,s] \xrightarrow {\sim } [0,u]$ is also a dyadic homeomorphism.
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