Definition talk:Connected (Topology)/Set

Is there any particular reason why this is called a "connected subset" while we have Definition:Closed Set (Topology)? --abcxyz (talk) 18:28, 16 December 2012 (UTC)


 * Good point. I think you're right. --Dfeuer (talk) 19:37, 16 December 2012 (UTC)


 * Because a closed subset of a topological space is called a "closed set of a topological space" but a connected subset is called a "connected subset of a topological space." --prime mover (talk) 22:07, 16 December 2012 (UTC)


 * "...is called": that is, by all (or some) of your source works? Even so, does anyone know why? By the way, at least one of my source works (Rudin) calls this a "connected set." --abcxyz (talk) 23:34, 16 December 2012 (UTC)


 * BTW, you should watch out with the name Rudin—there are two well-known mathematicians by that name, Mary Ellen Rudin and Walter Rudin. M.E. Rudin is mostly known for coming up with monstrous counterexamples to conjectures in topology, while Walter Rudin apparently focused on analysis. --Dfeuer (talk) 23:47, 16 December 2012 (UTC)


 * I meant Walter Rudin. So far, he's the only Rudin in Mathematicians. --abcxyz (talk) 23:53, 16 December 2012 (UTC)


 * AFAIK Mary Ellen Rudin has not written any texts, just a series of papers. Therefore it is perfectly appropriate to refer, when discussing texts, especially when the subject of conversation is the field of analysis, to "Rudin".


 * As for the naming convention of these various objects, I already spend a considerable percentage of what is laughably referred to as "free time" doing a considerable quantity of tedious refactoring, and I am thoroughly disinclined to arbitrarily rename stuff at the request of other contributors. Sometimes it makes sense to change the name of a page / concept, and sometimes I can't see the point. In the latter case I just find I've got other things I'd rather be doing. As I say, if this is an unacceptable attitude, then I can be voted out of my editing privileges with ease. --prime mover (talk) 06:58, 17 December 2012 (UTC)


 * First off, nobody is calling on you to do anything. I'm the one who initiated this in the first place, after all. As long as there are enough contributors who think the change is an improvement, and few enough who think it isn't, I'm perfectly happy to make the change (especially if somebody else doesn't want to).


 * Apparently, consistency (to some extent, of course) is desirable on this site. I (still) don't see any reason to call this a "connected subset" while most topological pages around (as far as I know) say "open set", "separated sets", etc.; hence the suggestion.


 * This is a minor point, but (formally) $H$ is not a subset of the topological space $T = \left({S, \tau}\right)$ itself, so the terminology "subset" does not seem the most appropriate here.


 * By the way, is there something you're trying to tell me by repeatedly bringing up being voted out of your editing privileges, or were you just in a bad mood at the times? I'm sorry, but I can't make anything out of this (except for "who the heck would do that?"). --abcxyz (talk) 04:44, 18 December 2012 (UTC)


 * This place is a democracy. Shrug. There are disagreements. Editing privileges are just that, privileges. If someone holds a point of view at variance with that of another, that person has the right to seek to terminate the privileges of that person by voting that they be removed from the website. Simple as that. --prime mover (talk) 06:25, 18 December 2012 (UTC)

IMHO the fine distinction between democracy and "oppression by the majority" needs to be hallowed. On-topic I have no distinguished opinion. For instance, in daily usage, "open set" in Dutch is literally phrased "open subset" so this dispute is linguistic rather than mathematical. --Lord_Farin (talk) 12:15, 18 December 2012 (UTC)


 * If the issue is linguistic, then what's the reason behind the inconsistency? --abcxyz (talk) 16:39, 8 January 2013 (UTC)


 * A complete distaste for going through and changing every single bloody page it appears on, because you can bet nobody else will bother, they'll expect me to bloody do it. Well I'm bloody not, so there. --prime mover (talk) 19:46, 8 January 2013 (UTC)


 * Sorry, I don't understand why we would need to change every single page it appears on. There are more than several pages that contain phrases such as "an open subset $U \subseteq X$". --abcxyz (talk) 16:11, 9 January 2013 (UTC)


 * History supports your claim, PM. I confess to several instances of that practice (although it be noted that most of the times I mainly want sb else's opinion). I have tried to cut down the tidy category several times, but I've since discovered that my value per time unit spent on PW is considerably higher when I develop new theorems or rewrite entire sections to match current vision statements (if you want, that's tidying as well, but it requires considerably more creativity and so is more appealing). --Lord_Farin (talk) 21:58, 8 January 2013 (UTC)

Issues with the definition of connected subset
Definition 1 is not equivalent to the other definitions. I assume books like Steen&Seenbach wanted to define another notion of connected subspace, which depends on the space. Connectedness in its most common and most useful sense (corresponding to the other definitions) is, morally, defined on spaces and not of subspaces. --barto (talk) 06:18, 10 March 2017 (EST)

Connected Subset vs. Connected Set
Having done a literature study, I find that "connected set" seems to be more prevalent than "connected subset", so I have taken the opportunity to replace "connected subset" with "connected set". As this is more general than "connected subspace", (as a subspace is always a subset, and a connected subspace is a connected set), I believe this is adequate. --prime mover (talk) 17:40, 17 January 2018 (EST)