Interlocking interval topology

In mathematics, and especially general topology, the interlocking interval topology is an example of a topology on the set S := R+ \ Z+, i.e. the set of all positive real numbers that are not positive whole numbers.

Construction
The open sets in this topology are taken to be the whole set S, the empty set ∅, and the sets generated by


 * $$ X_n := \left(0,\frac{1}{n}\right) \cup (n,n+1) = \left\{ x \in {\mathbf R}^+ : 0 < x < \frac{1}{n} \ \text{ or } \ n < x < n+1 \right\}. $$

The sets generated by Xn will be formed by all possible unions of finite intersections of the Xn.