\begin{definition}[Definition:Right Order Topology on Strictly Positive Integers]
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 $\Z_{>0}$'''.
\end{definition}