I need an example

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# I need an example

Submitted by shakir_bsm on Thu, 05/19/2005 - 09:08

Forums:

I am working on a project related to weak* topology.

Therefore I need an example of weak* topology.

please solve my this problem.

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## Versions

(v1) by shakir_bsm 2005-05-19

## Re: I need an example

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

## Re: I need an example

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.

## Re: I need an example

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.

## Re: I need an example

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.

## Re: I need an example

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!

## here is ur example

shakir u plz visit my society

i have a no of examples to give u

even from ur daily life

## Re: I need an example

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.