This result is known as the ultrafilter lemma. A variation of this statement for filters on sets is known as the ultrafilter lemma. Every ultrafilter on a compact Hausdorff space converges to exactly one point. Any ultrafilter containing a finite set is trivial. In ZF without the axiom of choice, it is possible that every ultrafilter is principal. An ultrafilter that does not contain finite sets is called "non-principal". If "S" is finite, each ultrafilter is principal. There are two very different types of ultrafilter&colon; principal and free. A principal (or fixed, or trivial) ultrafilter is a filter containing a least element. Instead, it relies on the intermediate Ultrafilter principle. The subset of "B" consisting of the former is called an ultrafilter of "B". Any ultrafilter that is not principal is called a free (or non-principal) ultrafilter. In this case "a" is called the "principal element" of the ultrafilter. Beginning with a structure, "A", and an ultrafilter, "D", form an ultrapower, "A". In this case, the non-principal ultrafilter is the set of all cofinite sets.