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Explicitly, a Boolean algebra is the partial order on subsets defined by inclusion (Skiena 1990, p. 207), i.e., the Boolean algebra of a set is the set of subsets of that can be obtained by means of a finite number of the set operations union (OR), intersection (AND), and complementation (NOT) (Comtet 1974, p. 185).
For example, a sigma-algebra is a collection of sets closed under countable union and a sigma-compact topological space is a topological space which is the union of countably many compact subsets. The symbol is also used to denote the divisor function.