(In a metric space:) Not of first category. This is not a joke! The Baire category theorem says that a complete metric space is of the second category.

The names "first category" and "second category" are known to be idiotic. But then, so is calling something "normal"...

Note to nuking editor: That really is all there is to say about second category. And it is an important concept (among other things, it's what makes things work in a Banach space).

Log in or registerto write something here or to contact authors.