ThmDex – An index of mathematical definitions, results, and conjectures.
Singletons are closed in Polish space
Formulation 0
Let $T = (X, \mathcal{T})$ be a D2299: Polish topological space.
Then \begin{equation} \forall \, x \in X : X \setminus \{ x \} \in \mathcal{T} \end{equation}
Proofs
Proof 0
Let $T = (X, \mathcal{T})$ be a D2299: Polish topological space.
This result is a particular case of R102: Singletons are closed in a metric space. $\square$