# Fσ set

In mathematics, an

**F**(said_{σ}set**F-sigma set**) is acountable union ofclosed set s. The notation originated inFrance with F for**' ("French": closed) and σ for**' ("French": sum, union).In

metrizable spaces, everyopen set is an F_{σ}set.The complement of an F

_{σ}set is a G_{δ}set. In a metrizable space, any closed set is a G_{δ}set.The union of countably many F

_{σ}sets is an F_{σ}set, and the intersection of finitely many F_{σ}sets is an F_{σ}set.For example, the set $A$ of all points $(x,y)$ in the

Cartesian plane such that $x/y$ is rational is an F_{σ}set because it can be expressed as the union of all the lines passing through the origin with rational slope::$A\; =\; igcup\_\{r\; in\; mathbb\{Q\; \{(ry,y)\; mid\; y\; in\; mathbb\{R\}\},$

where $mathbb\{Q\}$, is the set of rational numbers, which is a countable set.

**ee also**

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Set**— (s[e^]t), v. t. [imp. & p. p. {Set}; p. pr. & vb. n. {Setting}.] [OE. setten, AS. setton; akin to OS. settian, OFries. setta, D. zetten, OHG. sezzen, G. setzen, Icel. setja, Sw. s[ a]tta, Dan. s?tte, Goth. satjan; causative from the root of E.… … The Collaborative International Dictionary of English**set**— /set/, v., set, setting, n., adj., interj. v.t. 1. to put (something or someone) in a particular place: to set a vase on a table. 2. to place in a particular position or posture: Set the baby on his feet. 3. to place in some relation to something … Universalium**Set (game)**— Set! redirects here. Set! is also a special form in the Scheme programming language. Set is a real time card game designed by Marsha Falco and published by Set Enterprises in 1991. The deck consists of 81 cards varying in four features: number… … Wikipedia**set**— [ sɛt ] n. m. • 1893; mot anglais I ♦ Anglic. Manche d un match de tennis, de ping pong, de volley ball. Gagner le premier set. Partie de tennis en cinq sets. Balle de set, qui décide du gain du set. II ♦ Set ou set de table : ensemble des… … Encyclopédie Universelle**set**— Ⅰ. set [1] ► VERB (setting; past and past part. set) 1) put, lay, or stand in a specified place or position. 2) put, bring, or place into a specified state. 3) cause or instruct (someone) to do something. 4) give someone (a task) … English terms dictionary**set**— [set] vt. set, setting [ME setten < OE settan (akin to Ger setzen & Goth satjan < Gmc * satjan), caus. formation “to cause to sit” < base of SIT] 1. to place in a sitting position; cause to sit; seat 2. a) to cause (a fowl) to sit on… … English World dictionary**set*/*/*/**— [set] (past tense and past participle set) verb I 1) [T] to put someone or something in a position, or to be in a particular place or position Tea s ready, he told them and set down the tray.[/ex] She set the baby on the floor to play.[/ex] 2)… … Dictionary for writing and speaking English**Set**— (s[e^]t), v. i. 1. To pass below the horizon; to go down; to decline; to sink out of sight; to come to an end. [1913 Webster] Ere the weary sun set in the west. Shak. [1913 Webster] Thus this century sets with little mirth, and the next is likely … The Collaborative International Dictionary of English**Set**— has 464 separate definitions in the Oxford English Dictionary, the most of any English word; its full definition comprises 10,000 words making it the longest definition in the OED. Set may refer to:In mathematics and science:*Set (mathematics), a … Wikipedia**Set packing**— is a classical NP complete problem in computational complexity theory and combinatorics, and was one of Karp s 21 NP complete problems. Suppose we have a finite set S and a list of subsets of S. Then, the set packing problem asks if some k… … Wikipedia**Set-aside**— as a political measure was introduced by the European Union (EU) in 1988 to (i) help reduce the large and costly surpluses produced in Europe under the guaranteed price system of the Common Agricultural Policy; and (ii) to deliver some… … Wikipedia