Fσ is the same as in the Borel hierarchy.
Each closed set is an Fσ set.
The set of rationals is an Fσ set. Furthermore any countable set in a T1 space, is an Fσ set, because a singleton set is closed.
The set of irrationals is not a Fσ set.
The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set.
where , is the set of rational numbers, which is a countable set.
- Gδ set — the dual notion.
- Borel hierarchy
- P-space, any space having the property that every Fσ set is closed
- 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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