Definition talk:Jordan Arc

Change of definition
I would like to change the definition of the Jordan Arc so it only refers to an injective path. That is, remove the possibility that $f(0) = f(1)$. Then, the definition is compatible with what we define as an Definition:Arc (Topology).

Since it was myself who put in that definition (unsourced, I cannot recall from where), and the only theorems who use that definition was put up by myself, I should be able to correct these theorems.

If nobody has any objections, I'll change the definition during this week. --Anghel (talk) 14:32, 15 September 2022 (UTC)


 * If you can find a source work which defines it rigorously, that would allow me to rest easier -- but I appreciate that you may be flying blind, so to speak.


 * It's an obvious thing to say, but I will add that it is essential that its definition is compatible with however it is used in the (not many) pages that depend upon it. --prime mover (talk) 16:08, 15 September 2022 (UTC)


 * I know of a few source books which have pages available online which define Jordan Arcs. They all define it differently, but only the books about complex analysis allow a Jordan Arc to be non-injective at $f(0)$ and $f(1)$. I assume that was what made me write it as the main definition. I now believe that the topological definition should take priority, especially as it matches the definition of an arc.


 * I'll find a source online that I can quote, and then I'll write a very long 'Also defined as' section. There are only three theorems referring to the Jordan Arc, and they should be easy to alter. --Anghel (talk) 16:42, 15 September 2022 (UTC)


 * Take your time, and feel free to backtrack and sidetrack and forwardtrack again -- these things take time and thought and long pondering to get right. If there is such a thing as "right". --prime mover (talk) 18:13, 15 September 2022 (UTC)