
Re: Topologising a Group
Posted:
Nov 25, 2012 10:39 PM


On Sun, 25 Nov 2012, Shmuel (Seymour J.) Metz wrote:
> The previous contexst was one line, and not very helpfull: "Let F be a > filter over a group G, with e in /\F."
Let F be a filter base over a group G with e in /\F.
> What you meant by "For all g in G, let B_g = { gU  g in G }." For all g in G, let B_g = { gU  U in F }
Then B = { B_g  g in G } is a base for some topology tau on G.
If for all U in F, U^1 in F, then the inverse funciton is continuous.
If for all U in F, there's some V in F with VV subset U and G is Abelian, the the group operation is continuous.
If for all U in F, there's some V in F with VV subset U and for all g in G, U in F, gUg^1 in F, then the group operation is continuous.
Is there any better set of conditions, when given a base for e, that'll make a group a topological group?

