Much as a topological structure on a set is a notion of which subsets are ‘open’, so a bornological structure, or bornology, on a set is a notion of which subsets are ‘bounded’.
So far, we only discuss bornological topological vector spaces. See bornological set for the general notion of bornological space.
However, we can tell that bornological spaces and certain morphisms between them form a category .