What is the name of the complement of a nowhere dense set?

Question

Let $A$ be a nowhere dense set, what is the name of $A^c$? It seems much stronger than the definition of dense set. I think if we assume $A$ is a close set, then $A$ is nowhere dense iff $A^c$ is dense. But what about the general case?

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I found a long name for this: a dense set with dense interior. Does there exist a fancier name, probably named after a person?

Answer 1

A nowhere dense set is one whose closure has an empty interior.

Therefore the complement of a nowhere dense set is one whose interior has a closure that is the entire space.

Or, in other words, a set whose interior is dense.

Or, in yet other words, a superset of a dense open set.

Answer 2

Generic set is sort of usual. See the topology section of the linked page. But in Baire spaces this name is also used for co-meagre sets. I personally like generic set.