Communications of the
Korean Mathematical Society CKMS

We obtain some conditions for disconnectedness of a topological space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interrelations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.

Keywords: maximal open set, minimal open set, maximal closed set, minimal closed set, disconnected

MSC numbers: 54A05, 54D05