Timeline for Why is a certain projective limit of weighted symmetric Fock space, namely $\bigcap\limits_{\tau \in T, p\ge 1 } \mathcal{F}(H_\tau,p)$, separable
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| S Oct 6, 2023 at 15:05 | history | bounty ended | CommunityBot | ||
| S Oct 6, 2023 at 15:05 | history | notice removed | CommunityBot | ||
| Oct 1, 2023 at 8:54 | history | edited | CoffeeArabica | CC BY-SA 4.0 |
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| Sep 29, 2023 at 10:40 | history | edited | CoffeeArabica | CC BY-SA 4.0 |
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| Sep 29, 2023 at 10:34 | history | edited | CoffeeArabica | CC BY-SA 4.0 |
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| S Sep 28, 2023 at 13:42 | history | bounty started | CoffeeArabica | ||
| S Sep 28, 2023 at 13:42 | history | notice added | CoffeeArabica | Draw attention | |
| Sep 27, 2023 at 4:02 | comment | added | plm | Thank you. So i was right to expect being mistaken. :) So the most straightforward approach to fix that would be to pick some countable set of pairs of $\tau$ and $p$ that would yield the same intersection. Let's assume that we can restrict the weights $\tau_2$ to monic monomials. Perhaps we can also restrict to countably many sequences $(p_i)_i$, each $p_i$ a sequence, with $\left(\frac{1}{p_i}\right)_i$ a basis of square-summable sequences. Im sorry i don't feel like working it out now. I probably should not have commented in the first place if i was not going to do it right. Sorry. | |
| Sep 26, 2023 at 17:27 | comment | added | CoffeeArabica | Your family of intersections is uncountable tho. Since the index set is uncountable.. | |
| Sep 26, 2023 at 14:29 | comment | added | plm | If i'm not mistaken open subsets of $\mathcal{F}_{\text{fin}}(\mathcal{D})$ are intersections of $\mathcal{F}_{\text{fin}}(\mathcal{D})$ with some $\mathcal{F}(H_\tau,p)$; each of the latter spaces is separable as a subspace of a direct sum of separable metric spaces (the $n$th symmetric power). Then we can take the union of countably many dense sequences, one in each $\mathcal{F}(H_\tau,p)\cap\mathcal{F}_{\text{fin}}(\mathcal{D})$, which is dense in $\mathcal{F}_{\text{fin}}(\mathcal{D})$ and still countable. -This is superficial, as i don't know the background and may easily be mistaken. | |
| Sep 26, 2023 at 13:41 | history | asked | CoffeeArabica | CC BY-SA 4.0 |