Definition 8.5.7.12 (The Thompson Group). Let $\operatorname{Aut}_{ \mathrm{Dy} }( [0,1] )$ denote the collection of all dyadic homeomorphisms from the unit interval $[0,1]$ to itself. It follows from Exercises 8.5.7.10 and 8.5.7.11 that $\operatorname{Aut}_{ \mathrm{Dy} }( [0,1] )$ has the structure of a group (where the group law is given by composition of homeomorphisms). We will refer to $\operatorname{Aut}_{ \mathrm{Dy} }( [0,1] )$ as the *Thompson group*.

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