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I need an example

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I need an example

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I am working on a project related to weak* topology.
Therefore I need an example of weak* topology.
please solve my this problem.


In fact, one can define a topology by declaring which are the convergent sequences (more precisely the convergent nets). So we are speaking of the same thing simply in two different ways.
The advantage of mine is that in practice one has to know which kind of sequences converge!
For what concerns the construction of an example, I really don't understand what do you want: you just pick any vector space, make the dual and declare that you give it the weak* topology, isn't it?
Maybe more interesting could be to give an example of a sequence in the dual of a vector space which converges in the weak* topology and converges not in a "more usual" one...
Regards

I have studied that you write to me I need some mor guid line in constructing the example. I need such an example e.g for reflexive spaces the R_n is reflexive but l_1 is not reflexive.
Thanks.

Sir,
Actually I am student of BS(mathematics) in 6th semester.
In one of my assignments I need an example of weak* topology.
I think you are talking about the weak* topological space.
But I need weak* topology.When I am searching for weak* topology I have found an example that the standard topology on set of distributions D`(U) is weak* topology.
It is better for me if you give me an explanation of this example that what is the standard topology on the set of distributions.
Thanks.

hi
The defination that you described in your response is the defineation of weak* convergence.The weak* topology is the topology is the topology on dual of a norm space thatis defined by the class of semi norms on the dual of norm.
So this defination is creating trouble for me in construction of an example.
Please guide me in this.
Thanks.

It is really impossible to undersdand what you demand to me!
Very sorry!
If you explain better what you need, maybe I calud help you!

shakir u plz visit my society
i have a no of examples to give u
even from ur daily life

This is a topology given on the dual of a vector space V defined as follows:
A sequence f_n of linear functionals on V converges to the functional f if and only if
f_n(x)->f(x) for all x in V.
What do you mean by an example? By using the very definition you can build plenty of them!
Let me know if this answer to your question.
Best regards.

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