ThmDex – An index of mathematical definitions, results, and conjectures.
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▼ Zermelo-Fraenkel set theory
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▼ Topological space
Definition D249
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}
Results
▶ R4186: Complement of a G-delta set is an F-sigma set