A Strongly Connected Topology on the Mersenne Numbers

Resumen

In the present work, we introduce a new topology on the set of Mersenne numbers. This topology is Strongly Connected in the sense that it is hyperconnected and ultraconnected. Furthermore, to the best of our knowledge, this topology is the first non-trivial one defined on this set. Finally, with this topology, we characterize the infinitude of Mersenne primes.