Talk:Normed Vector Space with Schauder Basis is Separable

Been meaning to put this up for a while, thanks for getting to it. Still to do would be the case of an NVS over $\C$, which would be basically the same but use $\Q[i] = \Q + i \Q$ and its denseness in $\C$ instead of $\Q$. Caliburn (talk) 19:45, 16 October 2022 (UTC)

Yes, I think the denseness is the main hurdle here. Should be doable in a couple of days.--Julius (talk) 20:28, 16 October 2022 (UTC)

Duplicated results

Normed Vector Space over Complex Numbers with Schauder Basis is Separable is almost identical to this page, including their proofs.

This page is about vector space over $\R$, while the other page is over $\C$.

How about to merge these to one page about $\GF \in \set {\R, \C}$?

In the proof, it suffices to mention that $\GF$ is separable.

Ideally, create separate pages to state both $\R$ and $\C$ are separable. --Usagiop (talk) 21:37, 20 June 2023 (UTC)

Or, just saying $\GF$ has a dense subset $D$. For example, $D=\Q$ or $D=\Q \sqbrk i$. --Usagiop (talk) 21:41, 20 June 2023 (UTC)

Yep, I would say, like, let:

$D = \map D \GF = \begin{cases}\Q & \GF = \R \\ \Q \sqbrk i & \GF = \C\end{cases}$

Or similar. This is the approach I have applied for proofs where technically we have two cases, (real and complex) but only very very superficially. Caliburn (talk) 21:42, 20 June 2023 (UTC)