We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient… (More)

Some fundamental properties of maximal open sets are obtained, such as decomposition theorem for a maximal open set. Basic properties of intersections of maximal open sets are established, such as… (More)

Some properties of minimal open sets and maximal open sets are studied in [1, 2]. In this paper, we define dual concepts of them, namely, maximal closed set and minimal closed set. These four types… (More)