What does mean by $\text{refinement}$ in the following sentence ?
$\text{Ramification groups are a refinement of the Galois group G of finite extension of a field K. }$ given here-https://en.wikipedia.org/wiki/Ramification_group
I can not understand what is mean by $\text{refinement}$ i.e., $G \supset G_0 \supset G_1 \supset G_2 \cdots$
There is another concept of $\text{filtration}$ also.
Can you please explain the word $\text{refinement}$?
Do it same as refinement of open cover in topology?
"Refinement" is not used as a technical term in this context. Instead, it is just used (metaphorically) in the ordinary English sense of "a more fine-grained version". In other words, it is says that the ramification groups give more detailed information than you get from just the Galois group. More generally, it is common to refer to one invariant as a "refinement" of another if the first invariant gives "more information" than the second.