arXiv:2601.04256 · v4

The complexity of being monitorable

首次提交 2026-01-07 06:32

版本更新 2026-11-06 05:03

雷达观测 2026-11-09 10:16

摘要

We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the family of monitorable sets is $Π^0_3$ and determine the exact complexities it can have. In contrast, we show that if $X$ is not second countable then the family of monitorable sets can be much more complex, giving an example where it is $Π^1_1$-complete.