$F_{\sigma }$ set

A subset of a topological space is called a $F_{\sigma }$ set if it equals the union of a countable collection of closed sets.

The complement of a $F_{\sigma }$ set is a $G_{\delta }$ set (http://planetmath.org/G_DeltaSet).

For instance, the $X$ set of all points $(x,y)$ in the plane such that either $y=0$ or $x/y$ is rational is an $F_{\sigma }$ set because it can be expressed as the union of a countable set of lines:

$$X=\{(x,0)\mid x\in ℝ\}\cup \bigcup _{r\in \mathbb{Q}}\{(ry,y)\mid y\in ℝ\}$$

Title	$F_{\sigma }$ set
Canonical name	FsigmaSet
Date of creation	2013-03-22 14:37:59
Last modified on	2013-03-22 14:37:59
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	9
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 54A05
Related topic	G_DeltaSet
Related topic	G_deltaSet
Related topic	PavedSet
Related topic	PavedSpace