Abstract:This paper presents a topological approach to the study of rough automata.We introduce the core of a rough automaton and show that it naturally induces a topology on the state set. We show that this topology is preserved under the product of rough automata. We further establish topological characterizations of definite and possible primary subautomata in terms of regular closed sets. Based on these characterizations, we prove primary decomposition theorems for compact rough automata. Overall, this work clarifies the theoretical interplay among rough sets, topology, and automata.