It is well known and easy to see (modulo standard basic facts) that any compact 1-dimensional Alexandrov space with curvature bounded from below is isometric either to a circle or to a segment.


I am looking for a precise reference.



Isometric classification of 1-dimensional Alexandrov spaces
See 15.18 in our [Alexandrov geometry: foundations](https://arxiv.org/abs/1903.08539).


