Definition talk:Compact Space/Topology/Subspace

Does anyone agree that this should instead be called "compact set", as definition 2 makes no reference to the subspace topology? --abcxyz (talk) 19:04, 27 November 2012 (UTC)


 * We already have a redirect from Definition:Compact Set (Topology). I disagree with a rename because it's only definition 2 that makes no reference to the subspace topology. --prime mover (talk) 19:47, 27 November 2012 (UTC)


 * Sorry, but I still don't understand. As one need not consider the topological subspace $T_H$, I don't see why people should be bothered with the link as if it's essential to the definition.
 * I'm asking because of the current situation in Definition:Connected Topological Space. I think you'll agree that these two pages should use consistent terminology. --abcxyz (talk) 16:54, 1 December 2012 (UTC)


 * Sorry, are we talking about "compact" or "connected" here? The two are different concepts. Besides, I'm just about to get started on giving the connectedness field a rework anyway, as I said earlier - hold your horses, I'll get round to it in a bit. I've had other things to do this last few days (both personally and professionally) and my time for ProofWiki has been limited. --prime mover (talk) 20:48, 1 December 2012 (UTC)


 * I'm talking about compact subspace vs. compact set. The purpose of my mentioning the "connected" page was to just to make it clear that there is a reason I'm bringing this up. --abcxyz (talk) 21:48, 1 December 2012 (UTC)


 * I'm sorry, I don't see the connection. What is the connection (no pun intended) between what it says on the "connected" page with what it says on the "compact" page? What is this reason? I can't see it. --prime mover (talk) 22:31, 1 December 2012 (UTC)


 * Both concepts do not require, but can be defined in terms of, the corresponding topological subspace.


 * As I suggested before, my thinking is that if a particular definition does not use the topological subspace, the link should not be put in the beginning of the definition, as it can potentially leave people wondering ("where is that used?").


 * In short, I think it should more be like Definition:Connected Subset. Doing so also provides consistency. Comments? --abcxyz (talk) 18:27, 16 December 2012 (UTC)


 * I still can't understand what you're concerned about. --prime mover (talk) 22:05, 16 December 2012 (UTC)