Talk:Subbase

message: Wiki says.. 
The collection of open sets containing the empty set, X, and all finite intersections of elements of B forms a basis for T. 
And it seems to mean... 
{empry set} U {X} U {all finite intersections of elements of B}   is a basis for T.
From the less wordy one I wrote above, Is {empty set} really necessary? 
If so, it would be useful to explain in the article why it is necessary. 
Cosfly 07:09, 2 February 2007 (UTC)
thread_title:  Forms a basis only when it's with the Empty set??? 

message: The subbase consisting of all semi-infinite open intervals of the form (−∞,a) alone, where a is a real number, does not generate the usual topology. The resulting topology does not satisfy the T1 separation axiom, since all open sets have a non-empty intersection.
I don't follow this:  finite intersections of two of these guys yield (min(a,b),max(a,b)) and (-infty,a).  Is it saying that every union of these guys will be nondisjoint from every other union?  That's patently not true.  —Preceding unsigned comment added by 24.57.117.130 (talk) 18:21, 2 November 2007 (UTC)
thread_title: Subbase generated by (-infty,a) 

message: I've just encountered the term "semibase" instead of subbase, here: b:Topology/Bases#Semibases.  (The original formulation was a bit unclear; but, on the other hand, it is clear from the history, that the author first intended to use the term "subbase", but changed their mind.  This, I think, strongly suggests, that indeed the same concept was intended.)
Now, I personnally think the term "semibase" is more logical than "subbase" (since the latter term seems to indicate that we indeed have some kind of base); but this is of no real importance, compared to usage.  Thus, for the time being, I leave the term "semibase" on the wikibook page; but if this term was invented there and is only used there, then it should eventually be replaced.
On the other hand, if anyone has seen that "semibase" does appear in the literature (wikibooks uncounted:-), then the term should be mentioned at the start of this article, and a redir written from Semibase.  Thus, my question: Has anyone seen this alternative name used somewhere else? JoergenB (talk) 18:05, 13 August 2015 (UTC)
thread_title:  Has anyone seen "semibase" used as a synonym of subbase? 

message: I have restored a older version of the article for the following reasons.
The difference between the two versions consists essentially of approximately 50 edits by the same user, . The edit summaries do not allow to know if there is a significant content change between the two versions. Most changes deal with the presentation of the content. Many are simple changes of styles that ar forbidden by MOS:VAR, and also make very difficult to read the source of the article. All together, the edits change the encyclopedic style into a textbook style (see WP:NOTTEXTBOOK). In particular, definitions, theorems and other results are systematically presented in a quoted form. In Wikipedia, this may be convenient for the most importent results that require to be emphasized. Using this, as it has been done here, for recalling standard notations and results that are described in other articles is very confusing, since it makes difficult to find the main results (there are few in this article) and the significance of the definitions (this should be the most important part of this article). 
It is possible that some of these numerous edits are content improvement, but checking this is too time consuming, as this is not clear from edit summaries. D.Lazard (talk) 09:38, 4 October 2020 (UTC)
replies: text: Since you reverted my edit that fixed several technical details and removed redundant information, please fix these issues that you have reintroduced.Mgkrupa 17:12, 5 October 2020 (UTC)
replies: text:  It is to you to fix things that you think that need to be fixed. It is not the fault of other editors if you mix bold edits that are likely to be controversial with technical edits that hopely are not. Here there is a reorganization of the structure, and such reorganizations deserve always to be discuted. There is also, if I believe your previous post, several technical details, which are difficult to identify without spending time that would better be used elsewhere. So, if there are things to fix, fix them one after the other, with an edit summary that explains clearly each edit. If you think that this could be done better by another editor, explain clearly each issue in separated edit requests. D.Lazard (talk) 18:24, 5 October 2020 (UTC)
replies: text: Thank you D.Lazard.  Well said! PatrickR2 (talk) 04:35, 16 April 2022 (UTC)
thread_title:  Restoring an older version 

message: The "Alternate definition" section (added 11 Apr 2005 to the article) says that in some sources the definition of subbase requires that the collection of sets cover X.  As a sample source (added 13 Jun 2013) it gives a reference to the book "Topological Methods in Chemistry", written by two chemists from industry.
1. I propose to remove that source for the following reason.  The authors are not mathematicians.  As they themselves say in the preface of the book: 
:"The purpose of this book is to introduce a new method and language for investigating molecular structure based on finite topological spaces. It is not intended as a mathematical text ... We have eschewed the ... style typical of mathematical works in favor of the type of mathematical discourse commonly used in physical sciences."
I don't want to distract anything from the value of the book for its intended purpose, but I don't think it can be taken as an authoritative source for standard terminology/definitions in mathematics.
2. Can anyone provide a good mathematics source for this alternate definition?  The standard sources I have checked (Willard, Engelking, Dugundji, Arkhangelskii, ...) all use the first definition, i.e., without requiring that the collection of sets cover X.
If there is no such source, maybe the alternate definition should be removed from the article? PatrickR2 (talk) 05:26, 16 April 2022 (UTC)
replies: text: I removed the reference to "Topological Methods in Chemistry". PatrickR2 (talk) 21:12, 21 April 2022 (UTC)
thread_title:  Alternate definition section