\begin{definition}[Definition:Evenly Spaced Integer Topology]
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'''.
\end{definition}