Definition:Right Order Topology on Real Numbers

Definition
Let $\tau$ be the subset of the power set $\powerset {\R}$ be defined as:
 * $\tau := \O \cup \set {\openint a \infty: a \in \R} \cup \R$

Then $\tau$ is the right order topology on $\R$.

Hence the topological space $T = \struct {\R, \tau}$ can be referred to as the right order space on $\R$.

Also see

 * Right Order Topology on Real Numbers is Topology


 * Definition:Order Topology
 * Definition:Left Order Topology