User:Dfeuer/Definition:Usual Topology/Real Line

Definition 1
The usual topology on the reals is defined as the topology induced on $\R$ by the absolute value metric, which is the same as the Euclidean metric on $\R$.

Definition 2
The usual topology on the reals is defined as the topology generated by the basis consisting of all open intervals in $\R$ with the usual ordering. That is, the topology generated by the basis:


 * $\mathcal B = \{ (a \,.\,.\, b): a, b \in \R \}$

Definition 3
The usual topology on the reals is defined as the order topology on $\R$ with the usual ordering.