Solution
= Solution
Let $S_+=\{j:r_j>0\}$, nonempty since $R>0$. Every pair of distinct states in $S_+$ communicates directly, and no transition leaves $S_+$ for a zero-rate state. Hence \b[$S_+$ is the unique <closed communicating class>]. Each zero-rate state forms an open singleton: it has total departure rate $R>0$, goes into $S_+$, and can never be revisited. This includes the case that $S_+$ itself is a single absorbing state.