Definition talk:Admissible Family of Curves

I see how this is named, but it's counter-intuitive. It is the curves which are inadmissible, not the family. So "should" it really be "Family of Admissible Curves"?

Or has the technical language become standardised such that this is how it is referred as standard practice? --prime mover (talk) 07:57, 13 October 2022 (UTC)

The book says "admissible family of curves", but I cannot confirm yet that this is the standard title. I will look into this and if I find anything I will post that here.--Julius (talk) 08:13, 13 October 2022 (UTC)

It seems that both ways are acceptable. "Family of..." is used more often, and in general, phrases like [set,space,family] of admissible [...] are more abundant, but there are both old and new texts (articles, books, lecture notes) where both constructions appear. The question is what do want to stress more? "Admissible" means that the domain can be subdivided so that in every subdomain something is smooth, so a family is admissible because it is smooth on each open-closed rectangle. On the other hand, setting $s = const$ we pick a curve that is also admissible on each interval. I think whatever we choose is fine, just let's not forget to mention the other option under "Also known as".--Julius (talk) 10:48, 13 October 2022 (UTC)