weak topology

HMY

I'm trying to define the weak topology on the following Hilbert manifold
{ f: [0, 2pi] -> G s.t. f(0)=1 } where G is a connected Lie group.

What is the basis for the weak topology here?

If the dual space is { h : [0,2pi] -> Lie(G) }, I'm thinking the basis should be a finite
intersection of { h , subject to some conditions }. But this is where I start having
problems.

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HMY	weak topology Tweet I'm trying to define the weak topology on the following Hilbert manifold { f: [0, 2pi] -> G s.t. f(0)=1 } where G is a connected Lie group. What is the basis for the weak topology here? If the dual space is { h : [0,2pi] -> Lie(G) }, I'm thinking the basis should be a finite intersection of { h , subject to some conditions }. But this is where I start having problems.