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Is there a name for a family of sets that are all related by a subset-superset relationship? i.e. for any two sets in the family, their intersection is equal to at least one of them?

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    $\begingroup$ This sets are called totally ordered sets. $\endgroup$
    – little o
    Mar 29, 2019 at 18:42
  • $\begingroup$ “Totally ordered” can refer to any relation, not just the subset/superset relation. @Dbchatto67 $\endgroup$ Mar 29, 2019 at 19:35
  • $\begingroup$ But the sets which OP mentioned is also a special kind of totally ordered set where inclusion gives the ordering. $\endgroup$
    – little o
    Mar 29, 2019 at 19:38
  • $\begingroup$ @Dbchatto67 Yes, that’s true. It’s totally ordered by the inclusion relation. $\endgroup$ Mar 29, 2019 at 19:42

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It’s called a nested family of sets. See this answer for more information: https://math.stackexchange.com/a/1956996

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  • $\begingroup$ That's funny - I assumed there was a name, but if there hadn't been, I was going to call it a matryoshka family. $\endgroup$
    – ipetrik
    Apr 1, 2019 at 17:08

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