Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Topological space
F-sigma set
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $\mathcal{T}^{\text{op}}$ is the D2439: Set of closed sets in $T$
A D11: Set $E \subseteq X$ is an F-sigma set in $T$ if and only if \begin{equation} \exists \, F_0, F_1, F_2, \dots \in \mathcal{T}^{\text{op}} : E = \bigcup_{n \in \mathbb{N}} F_n \end{equation}
Formulation 1
Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
A D11: Set $E \subseteq X$ is an F-sigma set in $T$ if and only if \begin{equation} \exists \, (X \setminus F_0), (X \setminus F_1), (X \setminus F_2), \dots \in \mathcal{T} : E = \bigcup_{n \in \mathbb{N}} F_n \end{equation}
Dual definition
» G-delta set
Results
» R4186: Complement of a G-delta set is an F-sigma set