Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 220 / 1 / a / Solution

A compact real tree is a compact metric space $(T,d)$ such that any $x,y\in T$ are joined by a unique arc, and that arc is isometric to $[0,d(x,y)]$. The multiplicity of a point in a real tree $a\in T$ is the number of connected components of $T\setminus \{a\}$.