Abstract
We obtain some conditions for disconnectedness of a topolog- ical space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interre- lations 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.
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