Zulip Chat Archive

Stream: maths

Topic: Codisjointness

Yaël Dillies (Jun 05 2022 at 08:29):

Do people know the name of the dual property to disjointness? I'm introducing it in #14195 under the name codisjoint (to match docs#disjoint), but I'm making the name up because I've never seen it in the literature.

Yaël Dillies (Jun 05 2022 at 08:29):

cc @Yury G. Kudryashov

Bart Michels (Jun 05 2022 at 10:56):

Maybe "exhaustive"? https://en.wikipedia.org/wiki/Collectively_exhaustive_events

Yaël Dillies (Jun 05 2022 at 11:05):

Hmm... but this would go along with exclusive, not disjoint.

Mario Carneiro (Jun 05 2022 at 11:15):

Isn't this a covering set?

Reid Barton (Jun 05 2022 at 11:20):

Certainly a good word in spatial (or localic, etc) contexts. Maybe a little weird for e.g. subgroups of a group, but then disjoint also wasn't right in the first place

Junyan Xu (Jun 05 2022 at 20:34):

For ideals it's called coprime or comaximal, as in docs#ideal.mul_eq_inf_of_coprime and docs#ideal.quotient_inf_to_pi_quotient_bijective

This pair of notions also appears in https://en.wikipedia.org/wiki/Essential_extension (for modules)

Last updated: Dec 20 2023 at 11:08 UTC