Is the cofinite topology on a countable set first countable? I know it is not first countable on R but I don't know how to prove that it is first countable on a countable set.
2026-03-25 22:03:52.1774476232
How can I prove that the cofinite topology on a countable set is first countable?
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A countable set has only countably many finite subsets. And thus a cofinite topology on a countable set has only countably many open subsets. In particular it is both first and second countable.