Talk:Topological space

message: It was written "In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, that satisfy a set of axioms relating points and neighbourhoods." Then an anonymous editor (IP 173.28.211.0) did "...that satisfies a set of axioms" with edit summary "The first sentence had a grammatical error- it was written 'satisfy' whereas it should be 'satisfies' since the subject is 'a set'." I reverted, with summary "no, these two sets satisfy, together: of points, and of neighborhoods"; he/she reverted with summary "The words 'together with', 'along with', 'as well as' and 'in addition to' do not make the subject plural".
Being not a native English speaker, I do not argue. But I feel that the meaning is now distorted. Indeed, the axioms relating points and neighbourhoods cannot be satisfied (nor violated) but just points (nor by just neighborhoods); it should be meant that they are satisfied by points and neighbourhoods (in concert); thus, by the set of points and the set of neighbourhoods. Let someone competent is English and mathematics decide, what to do. Boris Tsirelson (talk) 09:39, 15 June 2016 (UTC)
replies: text: I think my modification may satisfy both.--Bill Cherowitzo  (talk) 17:10, 15 June 2016 (UTC)
replies: text: Nice. Boris Tsirelson (talk) 18:28, 15 June 2016 (UTC)
thread_title:  A word in the lead 

message: The initial line contains:
>  a topological space may be defined as
This is not as helpful to someone visiting that is looking to learn what the definition of "topological space" **is**.  To contrast with something specific, the Iron ore page begins with
> Iron ores are rocks and minerals from which...
not "Iron ores may be defined as rocks and minerals..."  I think the page would be improved if the sentence were changed to one of the following:
1. "a topological space is defined as..."
2. "There are several definitions for topological spaces.  Under <certain mathy conditions>, they are defined as..."
3. Something else that makes it clear what they are, not what they are permitted to be called.  — Preceding unsigned comment added by 198.45.19.113 (talk) 20:02, 11 March 2021 (UTC)
replies: text: Good point. The manual of style recommends "a topological space is ..." (I do not remember where it is recommended). I have fixed this, and by the way I have added at the beginning an informal definition that is, in fact, an explanation of the purpose of the concept. D.Lazard (talk) 21:06, 11 March 2021 (UTC)
thread_title:  "may be defined as..." 

message: In this article, "a topology" was defined as a collection of open sets. This goes against the common practice in mathematics. The true fact is that a collection of open sets defines a topology, but there are many other ways to define a topology. Many common topologies are not defined by their closed sets (for example, Zariski topology, topology of uniform convergence, etc.). I have edited the article and the redirect  for reflecting this. D.Lazard (talk) 11:45, 30 June 2022 (UTC)
thread_title:  Definition of  "a topology" 

message: The definition "any union (finite or infinite)" should specify "countable". 93.147.160.21 (talk) 11:01, 23 September 2022 (UTC)
replies: text: There is no such restriction in the standard definition. D.Lazard (talk) 13:19, 23 September 2022 (UTC)
thread_title:  Definition "any union (finite or infinite)" 

message: Is it just me or does it nowhere define a topological space? It only defines a topology TheGoatOfSparta (talk) 15:57, 23 September 2023 (UTC)
replies: text: The second sentence of the article is . This clearly a definition. Nevetheless , this definition should better be recalled in section . D.Lazard (talk) 17:23, 23 September 2023 (UTC)
replies: text: What I meant to say is that under the "definition via open sets" section it doesn't define a topological space. I wasn't specific. TheGoatOfSparta (talk) 09:30, 25 September 2023 (UTC)
thread_title:  Definition via open sets 

message: Can the neighbourhood M included in N be N? Does the neighbourhood M have to be the same for all neighbourhoods of x? TheGoatOfSparta (talk) 16:57, 23 September 2023 (UTC)
thread_title:  Definition via neighbourhoods