I want to know the answer to the following question:
What group uses infinite field extensions with topology?
All the background I'm provided with is that "Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions.". Is that enough to answer the question?
Answer: yes