Definition:Deleted Integer Topology

Definition
Let $\PP$ be the set:
 * $\PP = \set {\openint {n - 1} n: n \in \Z_{> 0} }$

that is, the set of all open real intervals of the form:
 * $\openint 0 1, \openint 1 2, \openint 2 3, \ldots$

Let $S$ be the set defined as:
 * $S = \ds \bigcup \PP = \R_{\ge 0} \setminus \Z$

that is, the positive real numbers minus the integers.

Let $T = \struct {S, \tau}$ be the partition topology whose basis is $\PP$.

Then $T$ is called the deleted integer topology.