Definition talk:Cofinal Subset

What are the restrictions on the relation? On the surface it appears that cofinal makes sense only on orderings, but there appears to be nothing to prevent any relation being used. In that case a set can only be cofinal with respect to the particular relation under discussion, in which case the notation will need amending appropriately. --prime mover 06:29, 24 November 2011 (CST)
 * The notion of a cofinal set is mostly related to partially ordered sets and appears a lot in the study of nets. However, the definition makes sense for any space that is endowed with a binary relation. It might not make much sense in practice but we need not assume that the underlying relationship is a partial order. --Pantelis Sopasakis 10:06, 25 November 2011 (EET)
 * Thx. Interesting. --prime mover 02:51, 25 November 2011 (CST)
 * Okay I've tidied it and added links, and moved the statement about $\N$ into a separate page where a proof needs to be added. --prime mover 03:03, 25 November 2011 (CST)

Rename suggestion

 * Cofinal Subset?
 * Cofinal Subset with respect to Relation?

I prefer the first one.

Also note we have Definition:Cofinal Relation on Ordinals which is also up for a rename and / or merging with this page.

Suggest we might do well to have this page as Definition:Cofinal/Subset and that page as Definition:Cofinal/Ordinals with Definition:Cofinal Subset and Definition:Cofinal Ordinals as redirects.

Thoughts? --prime mover (talk) 20:30, 17 July 2016 (UTC)


 * Cofinal Subset is fine. However, I wouldn't bother with subpages at this point. Once more material in this area is written, it's easy to reconsider if necessary. I would object against a merge (linking the two is a must, though). &mdash; Lord_Farin (talk) 20:58, 17 July 2016 (UTC)


 * Yep okay, job done. --prime mover (talk) 21:13, 17 July 2016 (UTC)