  We reformulate a key definition given by Wang and Agotnes (2013) to provide
semantics for public announcements in subset spaces. More precisely, we
interpret the precondition for a public announcement of {\phi} to be the "local
truth" of {\phi}, semantically rendered via an interior operator. This is
closely related to the notion of {\phi} being "knowable". We argue that these
revised semantics improve on the original and offer several motivating examples
to this effect. A key insight that emerges is the crucial role of topological
structure in this setting. Finally, we provide a simple axiomatization of the
resulting logic and prove completeness.
