The p-adic numbers and Hensel's lemma
The thesis consists of four chapters, each focused on developing the knowledge and drawing new connections with the p-adic numbers and the notions that are well known from the usual analysis on the real topology. In the first chapter, we introduce the basic structure of the $p$-adics, in connection to the conergent series and field axioms. Following that, in chapter two we focus on the defining t