Talk:Neighbourhood system
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Difference between a neighbourhood and a neighborhood
[edit]The following sentence invites us on a journey across oceans and cultures: "A neighbourhood of S in X is any subset T ⊆ X such that T contains some open neighborhood of S." Will someone qualified decide whether this page is to be written in British or American English? --Gabe — Preceding unsigned comment added by 135.180.2.43 (talk) 16:27, 7 January 2021 (UTC)
The union of local bases for all points x are a base for the topology
[edit]I don't see this being true. A neighbourhood of x (in the neighbourhood basis of x) may be closed - a base of the topology, however, only admits open subsets. Where does this come from? Quiet photon (talk) 08:39, 31 January 2011 (UTC)
Neighborhood filter undefined
[edit]The first Paragraph in Definitions mentions 'neighborhood filter' which is a link to this article which, as far as I can see, *nowhere* defines *what* a 'neighborhood filter' is. We are told that the neighborhood filter of a point is the same as the neighborhood filter of the singleton of that point, but not what the neighborhood filter *is*.
> Not an expert, but it appears that a 'neighborhood filter' is just another name for the neighborhood system (among others) which is simply calling attention to the fact that the neighborhood system happens to also be a filter. This is stated in the first line of the article. 65.128.22.54 (talk) 17:59, 19 February 2023 (UTC)
- You are right. This is stated in the Neighbourhood filter subsection:
The neighbourhood system for a point (or non-empty subset) is a filter called the neighbourhood filter for x
. It may be slightly confusing to have this terminology in the lead, but the reader can just take it at face value, given that the explanation comes later in the article. - As an aside, I think that the whole definitions section is a little too wordy and could be streamlined somewhat. Feel free to give it a shot. PatrickR2 (talk) 21:03, 19 February 2023 (UTC)
Too much duplication with the Neighbourhood article
[edit]It seems that about half of this article is a repeat of what's in the Neighbourhood article. This article should be trimmed down to what's specific about neighbourhood systems/filters/basis, and rely on links to the other article for the basics about neighbourhoods. PatrickR2 (talk) 05:00, 20 October 2022 (UTC)