Definition:Interlocking Interval Topology

Definition
Let $S = \R_{>0} \setminus \Z_{>0}$ denote the set of (strictly) positive real numbers excluding the positive integers.

Let $\BB$ be the family of sets $\family {S_n}_{n \mathop \in \Z_{>0} }$ defined as:
 * $S_n = \set {\openint 0 {\dfrac 1 n} \cup \openint n {n + 1} }$

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

$\tau$ is referred to as the interlocking interval topology.

The topological space $T = \struct {S, \tau}$ is referred to as the interlocking interval space.

Also see

 * Interlocking Interval Topology is Topology