Definition talk:Filter

Clash with directed set
@prime.mover do you remember where you got this? Condition (3) makes it different from a directed set (or subset), which is also known as a filtered set (as used in category theory), see e.g. Mac Lane, §IX.1 Filtered Limits. I trust you it comes from somewhere but it'd be helpful to know, perhaps there's an alternative name. --barto (talk) (contribs) 12:14, 8 January 2018 (EST)


 * This is the very common and universal definition of a filter. See WP for references. Instead it is "filtered set" which is less common than "directed set" in my encounters... Please bear in mind that MacLane's reference was written at a time when category theory was still very much in development. It might be that more recent works have standardised on "directed set". &mdash; Lord_Farin (talk) 12:46, 8 January 2018 (EST)
 * Thanks. I'm aware, I solely included "filtered set" because some sources use it. --barto (talk) (contribs) 12:52, 8 January 2018 (EST)