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

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

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $3$: Topological Spaces: $\S 2$: Topological Spaces: Example $7$