Talk:Continuous Image of Connected Space is Connected

Proof needs major rework
It's essentially incomprehensible to me, and I've already taken a semester of topology. This is a basic theorem, easy to prove from basic principles. --Dfeuer (talk) 03:55, 1 December 2012 (UTC)
 * Note: the concepts aren't difficult, really, but there are too many terms defined elsewhere, and there really shouldn't be any need to rely on other theorems. --Dfeuer (talk) 04:28, 1 December 2012 (UTC)


 * Currently, the theorem considers $f \left({T_1}\right)$ as a topological subspace of $T_2$, and hence there is a need to invoke the subspace topology and its properties, as well as use Definition:Connected (Topology) for $f \left({T_1}\right)$.


 * However, you might be thinking of $f \left({T_1}\right)$ as a set in the topological space $T_2$, in which case the definition in Definition:Connected (Topology) should instead be used for $f \left({T_1}\right)$.


 * Of course, the above two approaches to connectedness are equivalent, but (as of now) there isn't a page up which proves that. We just haven't done the job yet.
 * Once that has been done, then yes, I think a proof that uses the latter approach should be included (that is the one presented in Rudin).


 * Could you please clarify which parts of the proof are incomprehensible, in your opinion? --abcxyz (talk) 05:55, 1 December 2012 (UTC)


 * There could indeed be some sort of explanation added, even if just a link to another result, as to why $A \mid B \implies f^{-1} \left({A}\right) \mid f^{-1} \left({B}\right)$. Bear with me, I'm just about approaching this page in my current work package. --prime mover (talk) 08:11, 1 December 2012 (UTC)


 * I'd say that goes in the most general context possible, on Preimage of Partition is Partition or s.t. like that. --Lord_Farin (talk) 08:54, 1 December 2012 (UTC)

I think citing the "rule of transposition" is a great example of a bad idea: anyone who had a decent math class in middle school will know that rule, but probably won't know it goes by that name. Similarly, that awkwardly named theorem about inclusion could perhaps be linked to in some fashion that gives a clue about what it's saying and why it's relevant here. Just my two cents, and since I'm clearly too lazy to read the house style rules before passing go, collecting $200, or touching a proof, I guess those aren't worth much... --Dfeuer (talk) 09:07, 1 December 2012 (UTC)


 * Why would we want to compromise because people don't know things? There is a link, remember; at worst they will learn something. Some remark was in order, because we still had to invoke the rule of transposition.


 * I don't get your comment on the other invoked theorem. In any book, it'd pass as e.g. "by I.3.5, ..." over which I contend PW's take at it is an improvement. --Lord_Farin (talk) 09:17, 1 December 2012 (UTC)


 * Dfeuer: It is apparent that you have reservations about the quality of this website, for example its philosophy, house style, structure and (in several places at least) its content. We freely admit that there is indeed room for improvement, and indeed some of us are working hard to improve what we have. So here is a suggestion. You might want to start crafting, either in your own sandbox region or in a separate MediaWiki installation (or any architectural framework that you like, come to that) a demonstration model of how you would like ProofWiki to be.


 * I confess that the current structural philosophy of this website is mainly my brainchild, as I put together a lot of the initial groundwork and established the concept of minimal pages with maximal linking, and also the one-simple-statement-per-line presentational structure. I appreciate that, while I think this approach has a considerable amount to offer, it does not suit every user. But then if its structure were different, it would not suit those users who appreciate the style of ProofWiki.


 * In short, you appear to have come to a rugby match demanding to play cricket. --prime mover (talk) 09:31, 1 December 2012 (UTC)