Talk:Bounded set

message: I moved some talk that was here to Talk:Boundedness, since it was really about how to work (what became) that disambiguation page. This move frees this page for discussion specific to Bounded set. -- Toby Bartels 07:56, 2005 Mar 7 (UTC)
I moved some talk that was here to Talk:Bounded set (topological vector space), since it was really about that. This move frees this page for discussion specific to Bounded set in the basic meaning considered here. — MFH:Talk 21:35, 12 October 2006 (UTC)

message: moved to Talk:Bounded set (topological vector space) — MFH:Talk 21:35, 12 October 2006 (UTC)
thread_title: seminorms ?

message: moved to Talk:Bounded set (topological vector space) — MFH:Talk 21:35, 12 October 2006 (UTC)
thread_title: Set is bounded in locally convex space iff bounded under each semi norm

message: The opening line of the article is:
"In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size."
In no way, shape, or form does a bounded set imply a set be of finite size.  It really gives the wrong impression.  This should definitely be reworded. --anon
Well, "size" to most people means dimensions, or diameter. So, finite size means finite diameter. How do you see it yourself? Oleg Alexandrov (talk) 00:08, 21 February 2006 (UTC)
replies: text: And that's meant to be "informal description". Again, comments, suggestions, welcome. :) Oleg Alexandrov (talk) 00:09, 21 February 2006 (UTC)
thread_title:  Opening line 

message: Now that Bounded set (topological vector spaces) has its own article, it looks like this could naturally be split into Bounded set (metric spaces) and Bounded set (order theory). Boundedness of a set of real numbers is the only link between these two; maybe it should also have its own (expanded) article due its wide familiarity from calculus courses.
This is not really a proposal yet; I'd just like to see reactions.
—Toby Bartels (talk) 17:09, 25 August 2008 (UTC)
thread_title:  Split? 

message: So, an open interval of real numbers is bounded, am I correct? 
When searching maxima and minima over a convex set however it matters whether the edges are included or not. What is the n dimensional generalisation of the open/closed interval distinction called?
--80.98.242.95 (talk) 13:58, 7 August 2009 (UTC)
thread_title:  Boundedness vs open intervals 

message: Someone correct me if I'm wrong, but a non-metric topological space has a notion of boundedness based on set inclusion. I have in mind examples such as the Well-ordering Theorem (or axiom), or the recursive definition of the natural numbers, both of which depend on (or imply) boundedness. Am I, in some sense, comparing bananas and uglis? UrbanCyborg (talk) 00:44, 18 January 2019 (UTC)
thread_title:  Question on definition 

message: I think that the opening line, "a set is called bounded if it is, in a certain sense, of finite measure." is not good, especially with the wiki-link on measure.
I understand that in this sentence the word measure is supposed to be understood informally (with the idea that we actually mean diameter); but saying "finite measure" while pointing readers to measure (mathematics) really gives the wrong idea. Removing the link would be a minimum, however if we do so we can be sure that the link will be back sooner or later (especially with the new tools suggesting links to add).
I also understand that one might not want to be too specific because (1) this sentence is supposed to be non-technical and (2) we don't want to be too specific because we also want to include other notions of boundedness than the usual one in metric spaces. However I think that
* the second point is somewhat invalidated by the fact that the second sentence is "The word "bounded" makes no sense in a general topological space without a corresponding metric."
* something like "the distance between points cannot be arbitrarily large" is not overly technical, while being more accurate.
For now I'll remove the link on "measure", but I don't think it's a long-term solution. @Oleg Alexandrov, I saw you were involved previous discussions on this article — do you have any suggestions? (apropo: articolul ro:Mulțime mărginită are exact aceeași problemă; de fapt de asta am ajuns aici).
Best, Malparti (talk) 22:56, 10 January 2024 (UTC)
replies: text: I took the initiative of fixing the definition by changing "a set is called bounded if it is, in a certain sense, of finite measure" to "if all of its points are within a certain distance of each other". Malparti (talk) 10:47, 29 January 2024 (UTC)
thread_title:  Opening line