The quotient-circle norm is $\|x\|_{\mathbb R/\mathbb Z}=\min_{m\in\mathbb Z}|\widetilde x-m|$, independent of the chosen lift $\widetilde x$. A finite set is $\delta$-well-spaced when every two distinct points satisfy $\|x_r-x_s\|\ge\delta$. This is separation in the <circle metric>, including the distance across the identified endpoints.

Solution

Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 23 / 5 / a / Solution

 Solution (source code)