standard topology on $\mathbb {R}^n$

Question

When we talk about the "standard" topology on $\mathbb{R}^n$, does it mean the topology having basis as balls with the Euclidean distance, i.e:$d(x,y) = \sqrt{(x_1-y_1)^2+ \cdot \cdot \cdot + (x_n^2-y_n^2)}$?