In mathematics, an F σ set (said F-sigma set) is a countable union of closed sets. The notation originated in French with F for fermé (French: closed) and σ for somme (French: sum, union). [1] The complement of an F σ set is a G δ set. [1] F σ is the same as in the Borel hierarchy.

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定义2.3: 可数个开集的交集称为 G_\delta 集;可数个闭集的并集称为 F_\sigma 集.可数个 G_\delta 集的并集称为 G_{\delta\sigma} 集;可数个 F_\sigma 集的交集称为 F_{\sigma\delta} 集;以此类推下去.

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We now give definitions for two important types of subsets of $\mathbb{R}$ - $G_{\delta}$ sets and $F_{\sigma}$ sets. Definition: A subset $G$ of $\mathbb{R}$ is a $G_{\delta}$ -set if $G$ …

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6 天之前 · A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for fermé, meaning "closed," while the sigma stands for somme, meaning "sum."

Each open interval is an $F_\sigma$, but why is each open set an $F_\sigma$? An open set can be uncountable union of open intervals. If we are considering a general Borel sigma algebra instead of $B(\mathbb R)$, will each open set be an $F_\sigma$?