It doesn't -- that one was inspired by your question and is new as of today.

@ Gerhard: I don't know of any reference like that, although I did look for one when I was working on some of that research I cited in my answer. As far as I know, not much has been written on the "bijectively related" relation. I also don't know the answer to your other question, although it might be something good to think about.

@ Ramiro: Thanks for the suggestion -- I've added an answer to Henno Brandsma's original question that distills the relevant bits of this answer.

You're right -- I don't actually answer the question. Based on the question, I just thought that the asker might be interested in what I wrote. It was too long for a comment (and a brand new user can't comment anyway), so I posted it as an answer. I'll modify my answer above to reflect this. I'll also add a few thoughts that I've had since yesterday afternoon. (p.s.: Great question, Ramiro!)