I wanted to ask:

Is there a mathematical term for completing a collection of sets with the operations of intersection, union, and complement? In other words, all the regions of a Venn diagram of some sets.

Are such “word request” questions on-topic? By “word request,” I mean the OP has a mathematical object or result in mind, and wants to know if there’s an existing mathematical term for it.

Such questions are useful because once you know the name, you can Google it! Sometimes we genuinely don’t know if such an object even has a name. It can be really hard to find the right search results without one.