A simple triod is the union of three arcs that share one endpoint and are otherwise disjoint. The Moore triod theorem states that every pairwise disjoint family of simple triods in the plane is countable. One proof chooses data from a countable basis of open disks around each branch point; the Jordan curve theorem shows that two disjoint triods cannot determine the same finite basis data, giving an injection into a countable set of finite tuples.
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