Definition talk:Net (Preordered Set)

The first definition apparently does not allow for a definition of net convergence; this is the only sensible reason to introduce nets. As it is not citing any reference, I would like to delete it (Wikipedia and Conway both insist on a directed set). The diagonal relation (also known as the identity mapping) is a preorder, but not a directed set. It is obvious that no notion of convergence can be attached to this relation. Feel free to discuss. --Lord_Farin 09:52, 20 January 2012 (EST)

Not even realizing this page existed, I created Definition:Net (Set Theory), which I think is the definition Lord_Farin wanted. I'm not entirely sure that no one wants to use nets to talk about things other than convergence. Certainly Kelley defines them on general sets rather than just topological spaces (which is what Wikipedia does), but certainly a function on a directed set is a lot closer to the intuitive concept of a sequence than is a function on an arbitrary preorder. --Dfeuer (talk) 06:47, 18 December 2012 (UTC)

I admit I may have been too bold in my statements back then. It's just that I haven't encountered any evidence of the contrary.

Also, FFR, it is intended that my nickname be written with the underscore _. That MediaWiki software does not support this character in usernames is most annoying, but I don't know how to circumvent it. You are invited to abbreviate to LF, as most other regular contributors do. --Lord_Farin (talk) 12:14, 18 December 2012 (UTC)