Definition:Evenly Spaced Integer Topology

Definition
Let $\Z$ denote the set of integers.

Let $\BB$ be the set of sets defined as:
 * $\BB = \set {a + k \Z: a, k \in \Z, k \ne 0}$

where $a + k \Z := \set {a + k \lambda: \lambda \in \Z}$.

Then $\BB$ is the basis for a topology $\tau$ on $S$.

Then $\tau$ is referred to as the evenly spaced integer topology.

The topological space $T = \struct {S, \tau}$ is referred to as the evenly spaced integer space.

Also see

 * Evenly Spaced Integer Topology is Topology