Today I’ll continue the series on graded rings and filtrations by discussing the resulting topologies and the Artin-Rees lemma.

All filtrations henceforth are **descending**.

**Topologies **

Recall that a **topological group** is a topological space with a group structure in which the group operations of composition and inversion are continuous—in other words, a group object in the category of topological spaces. (more…)