A subset $G$ of a topological space $(X,\mathcal T)$ is open if it is an element of $\mathcal T$.
When $X$ is a metric space, a subset $A \subset X$ is open if and only if for all $a \in A$, there exists $\varepsilon > 0$ such that $B(a,\varepsilon) = {x \in X \mid \rho(a,x) < \varepsilon}\subset A$.
Wikidata ID: Q213363