Talk:Closure (topology)

message: Keeping in mind that every mathematical article requires some background necessary to begin considering the relevant ideas - this article (and a great many others) could benefit considerably by further explanation and expansion of the concepts.   This article, while clearly written by knowledgeable individuals, is too notation dense to be extremely useful - what I mean is that it lacks the critical element of sufficient, patient, explanations.  
I may suggest that this article can be substantially improved by diagrammatic examples and other devices (together with discussion) to expand upon the terse, notation-dense list given here.  
152.3.183.223 (talk) 17:02, 15 July 2010 (UTC)
thread_title:  Clarity of Explanation 

message: A separate article is titled closed set.  Should these two articles be merged?
-- Michael Hardy, 2003 Aug 12
I don't think so; conceptually they are quite different, since one is a property of sets, while the other is an operation on them.
To be sure, they are closely related and should be interlinked; but the concepts of open set, dense set, and the like are also closely related, yet separate.
We can afford to have an article on each of these, eventually expanding them all like Open set is now.
-- Toby Bartels 05:11, 25 Sep 2003 (UTC)
thread_title:  Closed set 

message: Is an adherent point of a topological space the same thing as a closure point? Surely a neighbourhood gives you an open set, and vice versa? Xanthoxyl 14:11, 12 March 2007 (UTC)
replies: text: Yes. Paul August ☎ 23:24, 9 July 2008 (UTC)
thread_title:  Adherent point 

message: Hi,
Regarding the present statement : 
"For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself)."
Would it be OK to clarify this in the following (or similar) way (OR would this be making the paragraph too long?): 
"For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself). Whether x is or is not a member of S depends on the space in which the closure is taken."
The motivation for this was the statement lower down that : 
"The closure of a set also depends upon in which space we are taking the closure. For example, if X is the set of rational numbers, with the usual subspace topology induced by the Euclidean space R, and if S = {q in Q : q2 > 2}, then S is closed in Q, and the closure of S in Q is S; however, the closure of S in the Euclidean space R is the set of all real numbers greater than or equal to \sqrt2."
Please let me know your thoughts,
Thanks
Arjun r acharya (talk) 11:05, 22 January 2009 (UTC)
thread_title:  Point of Closure 

message: I have recently added a number of references for this article. I selected a fairly broad spectrum of general (point-set) topology texts to use. One thing that they have in common is that none of them use the term "point of closure". Older treatments use the term "adherent point", but more modern texts drop the concept entirely and only talk about limit points. I would like to find a reference that actually uses the term "point of closure". Bill Cherowitzo  (talk) 18:53, 23 February 2014 (UTC)
thread_title:  Point of Closure 

message: In the last paragraph of part “Facts about closure”, it is mentioned that a certain notion of a “locally closed subset” coincides with the one of a closed set. However, there is already a different notion of a locally closed subset, which is different from the one discussed here. 
I think this expression should be replaced, because it is misleading (even though there are quotation marks). But I don’t know if there is a name for this property (which is equivalent to being closed, though) that could replace this awkward formulation. I’m thinking maybe we should just remove it. Any thought? 37.167.91.168 (talk) 18:18, 16 January 2023 (UTC)
thread_title:  “Locally closed subset”