Category:Relatively Prime Integer Topology

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This category contains results about Relatively Prime Integer Topology.

Let $\Z_{>0}$ denote the set of (strictly) positive integers.

Let $\BB$ be the set of sets $\set {\map {U_a} b: a, b \in \Z_{>0} }$ where:

$\map {U_a} b = \set {b + n a \in \Z_{>0}: \gcd \set {a, b} = 1}$

where $\gcd \set {a, b}$ denotes the greatest common divisor of $a$ and $b$.

Then $\BB$ is the basis for a topology $\tau$ on $\Z_{>0}$.


$\tau$ is then referred to as the relatively prime integer topology.

The topological space $T = \struct {\Z_{>0}, \tau}$ is referred to as the relatively prime integer space.

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