Opentopia Directory Encyclopedia Tools

F-sigma set

Encyclopedia : F : FS : FSI : F-sigma set


In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in France with F for fermé (French:closed) and σ for somme (French:union).

In metrizable spaces, every open set is an Fσ set.

The complement of a Fσ set is a Gδ set. In a metrizable space, any closed set is a Gδ set.

The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set.

 


From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.

Search Titles
0123456789
ABCDEFGHIJ
KLMNOPQRST
UVWXYZ?

E-mail this article to:

Personal Message: