A subset GGG of a topological space (X,T)(X,\mathcal T)(X,T) is open if it is an element of T\mathcal TT.
When XXX is a metric space, a subset A⊂XA \subset XA⊂X is open if and only if for all a∈Aa \in Aa∈A, there exists ε>0\varepsilon > 0ε>0 such that B(a,ε)=x∈X∣ρ(a,x)<ε⊂AB(a,\varepsilon) = {x \in X \mid \rho(a,x) < \varepsilon}\subset AB(a,ε)=x∈X∣ρ(a,x)<ε⊂A.
Wikidata ID: Q213363