Example · Graduate
Terms
| Term | This example | Why |
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| σ-algebra |
✗ |
The finite and cofinite subsets of $\reals$ do not form a σ-algebra. They are closed under complements and finite unions, but not countable unions: the union of the one-point sets $\setdef{n}$, for $n \in \nats$, is $\nats$, which is neither finite nor cofinite.
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| topology |
✗ |
The finite and cofinite subsets of $\reals$ do not form a topology, because they are not closed under arbitrary unions: the union of the one-point sets $\setdef{n}$, for $n \in \nats$, is $\nats$, which is neither finite nor cofinite.
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