Talk:Base (topology)

message: What's the difference between a base of T and the power set of T?
What's an example of a base that is not the set of all subsets of T?
...In the least number of dimensions possible, please; I am actually very stupid, no matter what my friends say.
Thank you. [curtsies]
Verdana♥Bold 13:48, 8 March 2016 (UTC)
replies: text: IMHO, talking about "the power set of T" and "the set of all subsets of T" (which are the same) does not make sense in this context. You need to reformulate your questions. --Beroal (talk) 07:15, 29 April 2017 (UTC)
thread_title:  Question from a padawan 

message: The introduction mentions T (B is a base wrt T if the unions of B equal T); while the formal definition doesn't make any reference.
TheZuza777 (talk) 19:45, 24 May 2017 (UTC)
replies: text: The formal definition doesn't make any reference to T because it is independent of T. B is a base on its own. "B is a base" is a term. You can read a statement in the article below the definition that B is a base iff the closure of B under unions (which may be named T) is a topology. This is how B is connected to topologies, but this is not a definition of base. "B is a base wrt T" is a different term. --Beroal (talk) 05:55, 25 May 2017 (UTC)
thread_title:  Introduction and definition do not match 

message: "In mathematics, a base (or basis) B of a topology on a set X is a collection of subsets of X that is stable by finite intersection."
* The collection should cover X
* The collection needs not be stable by finite intersection. A finite intersection is a union of some of its members, not necessarily one of its members (which is what "stable" means, right?)
Buiquangtu (talk) 05:30, 14 July 2020 (UTC)
replies: text: Thanks for pointing this incoherency between the lead and the body of the article. In fact, there are two different definitions, that of the lead and that of the article. The fact that the usual basis of the Zariski topology satisfies both definitions is probably the reason of this confusion. I have fixed the lead. D.Lazard (talk) 08:59, 14 July 2020 (UTC)
thread_title:  Confusing first phrase 

message: Problem with old intro is it was more technical than it had to be. The first line of the old intro was:
:In mathematics, a base (or basis)  of a topology on a set  is a collection of subsets of  such that every finite intersection of elements of  (including  itself, which is, by a standard convention, the empty intersection) is a union of elements of .
There is no need to mention the nullary intersection convention. The description involving finite intersections of sets in  is more technical than necessary for the intro. This technical description can be given later in the article. Mgkrupa 00:42, 23 October 2020 (UTC)
replies: text: Also, I'd like to see some well-known sources describe the nullary intersection convention as "a standard convention." Mgkrupa 00:45, 23 October 2020 (UTC)
thread_title:  Rewrote intro 

message: Hi, what is the application of "<" in "some<" in this sentence:
Thanks, Hooman Mallahzadeh (talk) 13:20, 15 December 2022 (UTC)
replies: text: This is certainly a typo introduced by inadvertently clicking on the corresponding button in the edit menu. To be removed. . D.Lazard (talk) 13:55, 15 December 2022 (UTC)
thread_title:  Please inspect the sentence