Abstract
Closure of Golomb's topology over the composite numbers provides a substantial condition for the infinitude of prime numbers in relatively prime arithmetic progressions.
Reference4 articles.
1. Dirichlet, P. G. L. (1837), ”Beweis des Satzes, dass jede unbegrenzte arithmetische Progres- sion, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthalt” [Proof of the theorem that every unbounded arith- metic progression, whose first term and common difference are integers without common factors, contains infinitely many prime numbers], Abhandlungen der Koniglichen Preusis- chen Akademie der Wissenschaften zu Berlin, 48: 45-71
2. Golomb, S. W. (1959). A Connected Topology for the Integers. The American Mathematical Monthly, 66(8), 663-665. doi:10.2307/2309340
3. Furstenberg, H. (1955). On the Infinitude of Primes. The American Mathematical Monthly, 62(5), 353-353. doi:10.2307/2307043
4. Szczuka, Paulina. (2014). Regular open arithmetic progressions in connected topo- logical spaces on the set of positive integers. Glasnik Matematicki. 49. 13-23. doi:10.3336/gm.49.1.02.