There is a natural question here: if E is an arbitrary subset of the real line, does it have a 'mass' or 'total length'?

T is closed under arbitrary joins (i.e. if a join of an arbitrary subset of T exists then it will be in T)

Let be an arbitrary subset of .

Support for modifying an arbitrary subset of a compressed texture, without having to re-download the whole texture to the GPU for significant performance improvements.

Owner Groups can be granted authority over arbitrary subsets of the object database, making it easy to slice up the network directory space in any fashion that may be desired.

There is a corresponding notion of smooth map for arbitrary subsets of manifolds.

Indices may be created on arbitrary subsets of the attributes in a table.

Constructing takes exponential time in the number of tasks, since is not constrained and arbitrary subsets of must be considered.

The set of accept states can be taken to be some arbitrary subset of the topological space.

For example, to study an arbitrary subset of A of Euclidean space, one may instead replace it by a union of dyadic cubes of a particular size that cover the set.