Moniker1998 comments

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                                            Moniker1998

Weak topology on $\ell^2$ is an $\aleph_0$-space

@StevenClontz what exactly are you alluding to? I'm not exactly sure what is non-topological that needs explaining here. I could explain it if need be, since I did study functional...

Weak topology on $\ell^2$ is an $\aleph_0$-space

Below is a proof that weak-* compact subsets of $X'$ are norm-bounded: Let $C$ be a weak-* compact subset of $X'$. Since for $x\in X$ the map $T\mapsto T(x)$ from...

Weak topology on $\ell^2$ is an $\aleph_0$-space

@prabau If we are to add that S21 has countable $k$-network then one should also delete that its an $\aleph_0$-space because of redundancy. Also we should decide if we want...

Weak topology on $\ell^2$ is an $\aleph_0$-space

I think that this seemingly elementary proof might be more trouble than its worth, and one should just cite the original paper by E. Michael.

Weak topology on $\ell^2$ is an $\aleph_0$-space

I see what you mean now. As for citing all those theorems from functional analysis, rather than citing wikipedia I'd be more content with citing one book about functional analysis...

Pseudocompactness-like property

https://mathoverflow.net/questions/479319/pseudocompact-spaces-and-locally-finite-open-covers alright. I've distinguished 2 properties from this actually, $P_1$ and $P_2$. $(P_1)$: Every locally finite cover has finite subcover $(P_2)$: Every locally finite cover is finite theorems I would...