User:Dfeuer/Definition:Usual Topology/Rn

Definition 1

Let $n$ be a strictly positive natural number.

Let $\R$ be the set of real numbers.

The usual topology on $\R^n$ is the topology induced by the Euclidean metric on $\R^n$.

Definition 2

Let $n$ be a strictly positive natural number.

Let $\R$ be the set of real numbers.

The usual topology on $\R^n$ is the product topology on the product $\ds \prod_{i \mathop = 1}^n \R$ where each factor is given the User:Dfeuer/Definition:Usual Topology/Real Line.