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Topic: Topologising a Group
Replies: 6   Last Post: Nov 25, 2012 10:39 PM

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William Elliot

Posts: 1,533
Registered: 1/8/12
Re: Topologising a Group
Posted: Nov 25, 2012 10:39 PM
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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?




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