ThmDex – An index of mathematical definitions, results, and conjectures.
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
Open set
Closed set
Definition D2640
Clopen set
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
A D11: Set $E \subseteq X$ is clopen in $T$ if and only if
(1) $E \in \mathcal{T}$ (D97: Open set)
(2) $X \setminus E \in \mathcal{T}$ (D98: Closed set)