About: 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: 1. * The union of open sets is an open set. 2. * The finite intersection of open sets is an open set. 3. * S and the empty set ∅ are open sets.