 The idea is that if w is the actual world, then agent a has the information that the actual world must be one of those in her connected component \(\cc_a(w)\). Thus the set \(\cc_a(w)\) makes up the worlds agent a considers to be possible whenever w is the actual world. And since \(w\in\cc_a(w)\), agent a will always consider the actual world to be possible. Local connectivity then guarantees that the agent always has an opinion as to the relative plausibility of any two worlds among those in \(\cc_a(w)\) that she considers possible. 