Some topological properties of the profinite group of p-adic Integers Zp - Santos, Juan Paolo C. (College of Science, University of the Philippines Cebu, 2022)
In this paper, we introduce the set of p-adic integers Zp from two different perspectives: (1) a subset of the set of p-adic numbers Qp, and (2) as the set of all equivalence classes of Cauchy sequences on Z with respect to the p-adic absolute value. We then show that the p-adic integers is a profinite group. In this paper, we also verify that profinite groups are compact and totally disconnected topological groups and thus, we also show that indeed, the p-adic integers as a profinite group, is compact and totally disconnected using its formal definition.