Talk:Path as Parameterization of Contour
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Jordan Arc or Jordan Curve
Isn't a Jordan curve an instance of a Jordan arc -- the one which just happens to have $\map f 0 = \map f 1$?
In this case can we not just say "Jordan arc" and then slap together some boilerplate "A Jordan curve is an instance of a Jordan arc so anything that applies to a generic Jordan arc also applies to a Jordan curve as well.
We surely don't need to write "Jordan arc or Jordan curve" everywhere. Sorry, not only does it make it look clumsy, but people will then want to know what the difference is between the concepts that causes there to be a distinction to be made between the two. --prime mover (talk) 23:19, 16 September 2022 (UTC)
- A Jordan curve is no longer an instance of a Jordan arc, because I have just changed our definition of Jordan arc so it matches with what we define as an Definition:Arc (Topology). The only sources I could find that considered a Jordan curve to be a Jordan arc were those dealing with complex analysis, so yes, there will be some clumsy sentences in the cross-references from complex analysis to Jordan arcs. (Same thing with simple, which means something else in complex analysis than it does in topology.) Of course, I've written a long paragraph describing the different definitions of Jordan arcs.
- There were only three theorems that directly referenced Jordan arcs, and I believe I introduced them all ten years ago, so it won't change much in the structure of the wiki. Also, the original version of the definition said that Jordan arcs were injective, and it was myself who changed it (because I only checked complex analysis sources), so I have more or less reverted back to our original definition. --Anghel (talk) 21:53, 17 September 2022 (UTC)
- Yes okay I'll leave this then, I need to get back up to speed on complex analysis, it occurs to me that I'm not close enough to it to judge. I see Copson confirms your take on this, Priestley is unreadable, and I can't find my Stewart and Tall. --prime mover (talk) 22:18, 17 September 2022 (UTC)