
Furstenberg's
topology
and
his
proof
of
the
infinitude
of
primes
Title: 
Furstenberg's topology and his proof of the infinitude of primes 
Author:

Manuel Eberl

Submission date: 
20200322 
Abstract: 
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
(wellknown) facts are formally proven, including an explicit metric
for the topology given by Zulfeqarr. 
BibTeX: 
@article{Furstenberg_TopologyAFP,
author = {Manuel Eberl},
title = {Furstenberg's topology and his proof of the infinitude of primes},
journal = {Archive of Formal Proofs},
month = mar,
year = 2020,
note = {\url{http://isaafp.org/entries/Furstenberg_Topology.html},
Formal proof development},
ISSN = {2150914x},
}

License: 
BSD License 
Status: [ok] 
This is a development version of this entry. It might change over time
and is not stable. Please refer to release versions for citations.

