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. To give the set S a topology means to say which subsets of S are "open", and to do so in a way that the following axioms are met:
- The union of open sets is an open set.
- The finite intersection of open sets is an open set.
- S and the empty set ∅ are open sets.
The open sets in this topology are taken to be the whole set S, the empty set ∅, and the sets generated by
The sets generated by Xn will be formed by all possible unions of finite intersections of the Xn.
- Steen & Seebach (1978) pp.77 – 78
- Steen & Seebach (1978) p.3
- Steen & Seebach (1978) p.4