Let X be a set whose members are all non-empty.

In the category of non-empty sets, there are no initial objects.

Let X be a non-empty set and G a group.

Every free action on a non-empty set is faithful.

In computer science, an alphabet is a finite non-empty set.

Note that P is not required to be non-empty.

It is also easy to see that every non-empty set in is infinite.

This, in particular, shows that for any non-empty set, there is always a metric space associated to it.

Recall that an order ideal is a (non-empty) directed lower set.

In a strict sense, bounces sent with a non-empty are incorrect.

If the b -boundary is non-empty, there are only two possibilities.

Thus no non-empty set T exists and the required result is thereby proved.

AC states that every collection of non-empty sets must have a choice function.

This is allowed as, by assumption, the set is non-empty.

W: Every non-empty set of positive integers contains a least member.

However not all authors insist on the underlying set of a semigroup being non-empty.

Every non-empty set of points (with no duplicates) has at least one centerpoint.

A space is hyper-connected if no two non-empty open sets are disjoint.

Thus it is non-empty which is just what the axiom of choice states.

In other words, every non-empty subset of an indiscrete space is dense.

Informally it states that one can simultaneously choose an element from every non-empty set.

Hence, the theory is implicitly taken to be non-empty.

Harmonic mean for a non-empty collection of numbers a, a, .

So every subgame of v has a non-empty core.

A domain of discourse D, usually required to be non-empty (see below).