Definition:Right Order Topology on Strictly Positive Integers

Definition
Let $\Z_{>0}$ be the set of strictly positive integers.

For $n \in \Z_{>0}$, let $O_n$ denote the set defined as:
 * $O_n := \set {x \in \Z_{>0}: x \ge n}$

Let $\tau$ be the subset of the power set $\powerset {\Z_{>0} }$ be defined as:
 * $\tau := \O \cup \set {O_n: n \in \Z_{>0} }$

Then $\tau$ is the right order topology on $\Z_{>0}$.

Hence the topological space $T = \struct {\Z_{>0}, \tau}$ can be referred to as the right order space on $\Z_{>0}$.

Also see

 * Right Order Topology on Strictly Positive Integers is Topology


 * Definition:Order Topology
 * Definition:Left Order Topology