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

• Results about the right order topology can be found here.