Definition:Right Order Topology on Strictly Positive Integers
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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
- 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 $7$