Countable complement topology
= Countable complement topology
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= Cocountable topology
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The open sets are the empty set and subsets whose complement is countable. On an uncountable set, any two nonempty open sets intersect, so the space is not <Hausdorff>. On a countable underlying set this topology is discrete. The <compact subsets of a cocountable space> are finite, regardless of the cardinality of the underlying set.