TITLE: How are inclusion-wise maximal and minimal sets defined?
QUESTION [10 upvotes]: I have tried to find them over the internet, but am lacking a resource that rigorously defines these two terms.

REPLY [22 votes]: An inclusion-wise maximal set among a collection of sets is a set that is not a subset of some other set in the collection. An inclusion-wise minimal set among a collection of sets is a set in the collection that is not a superset of any other set in the collection.