Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Σ), it is used as a symbol for sums and series. As a lower case letter (σ) it is a prefix used in several contexts to indicate that a term is referred in some way to countable unions. For example, a σ-algebra is a collection of sets closed under countable union and a σ-compact topological space is a topological space which is the union of countably many compact subsets. The symbol σ_k(n) is also used to denote the divisor function.