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Ganesh
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Finite Topology vs sigma Field

Suppose we have a finite $\sigma$ -field $S$, of which $A$ and $B$ are member sets. Since $S$ is closed under union and complementation [by definition], it follows that $(A' \cup B')' = (A \cap B)' \in S$. From closure under complementation, we have that $A \cap B \in S$, implying that $S$ is closed under intersections.

Does it follow that every finite $\sigma$ -field is a topology?

Ganesh
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