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)