# Euclidean topology

In any metric space, the open balls form a base for a topology on that space.[1] The Euclidean topology on Rn is then simply the topology generated by these balls. In other words, the open sets of the Euclidean topology on Rn are given by arbitrary union of the open balls ${\textstyle B_{r>0}(p)=\{x\in \mathbb {R} ^{n}\mid d(x,p), for all ${\displaystyle p\in \mathbb {R} ^{n}}$, where d is the Euclidean metric.