The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set. Fσ is the same as in the Borel hierarchy.
Each closed set is an Fσ set.
The set of rationals is an Fσ set. The set of irrationals is not a Fσ set.
In a Tychonoff space, each countable set is an Fσ set, because a point is closed.
where , is the set of rational numbers, which is a countable set.
- Stein, Elias M.; Shakarchi, Rami (2009), Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, p. 23, ISBN 9781400835560.
- Aliprantis, Charalambos D.; Border, Kim (2006), Infinite Dimensional Analysis: A Hitchhiker's Guide, Springer, p. 138, ISBN 9783540295877.
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