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

For $s,t\in [0,1]$, defineThe function $d_g$ is a pseudometric. Declare $s\sim t$ when $d_g(s,t)=0$, and give the quotient set $T_g=[0,1]/\sim$ the induced metric, again denoted $d_g$. This is the real tree encoded by an excursion $g$.