11 questions linked to/from Dual of $l^\infty$ is not $l^1$
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### Applications of ultrafilters

I'm looking for some interesting applications of ultrafilters and also everything of interest involving ultrafilters. Do you know some applications or interesting things involving ultrafilters? I'm ...
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### Basic facts about ultrafilters and convergence of a sequence along an ultrafilter

Could you help, please. I need the information about the ultrafilters, namely, any ideas how one can see that they exist and a proof of the fact that for any ultrafilter every sequence on a compact ...
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### Where has this common generalization of nets and filters been written down?

It is well-known that there are two different ways to generalize the theory of convergence of sequences to arbitrary topological spaces: nets and filters. They are of course essentially equivalent, ...
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### Nonnegative linear functionals over $l^\infty$

My purpose is a clarification of the role of the axiom of choice in constructing limits for bounded sequences. Namely, we want a linear functional of norm 1 defined on the space of all bounded complex ...
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### Dual of $\ell_{\infty}$ is not $\ell_1$

As the title indicates I'm trying to show that $\ell_{\infty}^{*}$ is not $\ell_1$. I've shown that for p, q conjugate and finite we do indeed have $\ell_{p}^{*} = \ell_q$, with the correspondence ...
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### continuous linear functional on $l^{\infty}$ space
Let $l_{\infty}$ be the space of all bounded complex-valued sequences equipped with the supremum norm. Consider the natural standard basis $\{e_n\}_{n \in \mathbb{N}}$ of $l_{\infty}$. For any ...