Talk:Closed Real Interval is Compact/Topological Space

Added this page after discussion in Talk:Closed Bounded Subset of Real Numbers is Compact/Proof 1. I set this as Proof 1 in Closed Real Interval is Compact (and shifted the other two proofs accordingly) in order to display the proofs in ascending order of specificity (descending order of generality). I've amended the end to make clear that the definition of compact being used is the topological one (Definition:Compact Space/Real Analysis/Definition 2; although perhaps it should be Definition:Compact Space/Topology directly?). Perhaps this should also be made clear in the "theorem" section? (Right now it copies the theorem from the disambiguation page, Closed Real Interval is Compact).

Ah right okay, we need to refactor this because as I said in another place the numbering/naming of this area is suboptimal. You probably missed seeing that.

The whole point here is that these proofs are not equivalent, because they are not on the same domains, hence naming them "Proof 1" and "Proof 2" was already, um, trying to hunt for a polite synonym for "stupid" and failing.

When I get round to it I will refactor this area. --prime mover (talk) 12:28, 17 April 2021 (UTC)

Also, regarding the sources: this was taken verbatim from Closed Bounded Subset of Real Numbers is Compact/Proof 1. It's only a part of a proof in a theorem from the Sutherland book. I think it would be good to add a reference; but a static reference/citation, one that doesn't interfere with the next/prev system but still acknowledges the source of the work. I don't know if that's possible or how that would be done. --Plammens (talk) 12:18, 17 April 2021 (UTC)

Don't worry about it, leave it and I'll get to it in due course. --prime mover (talk) 12:28, 17 April 2021 (UTC)