Semi-normed and normed groups \(\newcommand{\mmm}{\mathfrak{m}} \newcommand{\qqq}{\mathfrak{q}} \newcommand{\rr}{\mathbb{R}} \newcommand{\rnneg}{\rr_{\geq 0}} \newcommand{\rpos}{\rr_{> 0}} \newcommand{\zz}{\mathbb{Z}} \newcommand{\znneg}{\zz_{\geq 0}} \)All groups are going to abelian with the group operation denoted by “+”. A filtration, a generalization of valuation, is a function \(\nu\) from a group \(G\) to \(\rr \cup \{\infty\}\) such that Filtrations are in one-to-one correspondence with ultrametric functions… Continue reading Notes (part 1): S. Bosch, U Güntzer and R. Remmert, Non-Archimedean Analysis