Talk:Filter on a set

Very long

This article was created in May 2022 using content from Filter (mathematics) and Filters in topology, but the resulting article is very long with a wikitext size of about 141 KB. I'd suggest condensing the proofs and longer paragraphs. –LaundryPizza03 (dc̄) 05:21, 26 March 2023 (UTC)

To add insult to injury, this article was created by copying content from Filters in topology, but that content there was not deleted. So now we seem to have two articles saying the same things, which would make them unmaintainable (errors/fixes in one don't automatically show up in the other.) There must be a better way. 67.198.37.16 (talk) 22:33, 30 April 2023 (UTC)

Merge proposal

I propose merging Ideal (set theory) into Filter (set theory) because the two concepts are perfectly dual to each other so the separate articles are redundant. Jean Abou Samra (talk) 15:33, 19 September 2025 (UTC)

I don't know if that's a good idea. The article "Ideal (set theory)" is of manageable size and readable. The article "Filter (set theory)" is really not a good encyclopedic article. It was essentially highjacked by one user (Mgkrupa) to use as his own repository of the most minute information about the topic, to the extent that the article became pretty much inaccessible to any but the most determined of mathematicians already familiar with the topic. Merging Ideal into here will make the information about ideals similarly inaccessible. PatrickR2 (talk) 03:46, 23 September 2025 (UTC)

@Jean Abou Samra And by the way, just noticed it now, thanks for all the trimming you have been doing already to this article. PatrickR2 (talk) 03:54, 23 September 2025 (UTC)

@PatrickR2 Agreed, it was quite unreadable. But I've completely rewritten it over the past week (mostly after you wrote your comments). I hope it is digestible at this point, and it would be much easier than in the previous state to incorporate ideals into it. Jean Abou Samra (talk) 11:41, 29 September 2025 (UTC)

I mean, we have separate articles (and to be clear, we should have separate articles) for open set and closed set, so just being dual notions is not in itself a good enough reason to merge. I think the contexts in which ideals and filters are used are fairly different; for example, you speak of a generic filter for a forcing notion, not a generic ideal. You could talk about generic ideals, but you just don't. Conversely, it's usually ideals, not filters, that are used to form quotient Boolean algebras, and we talk about P-ideals but not, as far as I know, P-filters.

That said, a merge wouldn't be the worst thing in the world. But I'd need more convincing than just saying "they're dual notions". --Trovatore (talk) 04:30, 23 September 2025 (UTC)

Good point. It's true that the contexts are fairly different, however I think that the content we want to put in these specific pages is mostly the same (with everything dualized), as opposed to the content on a page like generic filter about a specific application, which should just use whichever one of the two makes more sense in that context. Looking at the current content on Ideal (set theory), incorporating it into this page would add very little text overall, e.g., most of the examples are already here too (and not just because I ported a couple in my recent rewrite of this page). Jean Abou Samra (talk) 12:00, 29 September 2025 (UTC)

I'm generally not a fan of foo and foo-dual pages because they don't describe a single sort of object. I have to admit that they sometimes do seem to be the best solution, but it's never the first tool out of the box for me. I would want to see some compelling reason to do it, not just an argument that it could be done. --Trovatore (talk) 21:05, 29 September 2025 (UTC)