Email Gateway (Aug 23 2022 at 08:34): Email Gateway (Aug 23 2022 at 08:34):From: "Thiemann, René" <Rene.Thiemann@uibk.ac.at>
Dear all,
I’m happy to announce a new AFP entry by Manuel Eberl.
Furstenberg's topology and his proof of the infinitude of primes
This article gives a formal version of Furstenberg's topological proof of the infinitude of primes. He defines a topology on the integers based on arithmetic progressions (or, equivalently, residue classes). Using some fairly obvious properties of this topology, the infinitude of primes is then easily obtained.
Apart from this, this topology is also fairly `nice' in general: it is second countable, metrizable, and perfect. All of these (well-known) facts are formally proven, including an explicit metric for the topology given by Zulfeqarr.
More details at: https://www.isa-afp.org/entries/Furstenberg_Topology.html
Enjoy and stay healthy,
René
Last updated: Nov 21 2024 at 12:39 UTC