singletons

In mathematics, a singleton (plural: singletons) is a set containing exactly one element. For example, the set {x} contains the single element x. Singletons are the simplest non-empty sets and arise in various contexts, such as in topological spaces and probability theory, where a singleton can represent a degenerate event with probability one. The concept also appears in other areas of mathematics as a basic building block.

In computer science, the singleton pattern is a design pattern that restricts a class to a single instance and provides a global access point to that instance. This pattern is intended to ensure that only one object represents a particular resource or coordination point within a program.

This pattern is commonly implemented through a private constructor and a static field or method that holds the sole instance, with consideration for when the instance is created (eager versus lazy) and whether multiple threads may access it concurrently. Variants exist, including double-checked locking and language-specific constructs such as object declarations or enumeration-based singletons. Care is required to guard against serialization or reflection bypass, which can create additional instances.

Critics argue that singletons introduce global state, complicate unit testing, and increase coupling. Alternatives include dependency injection, explicit lifetimes managed by modules or services, or simply passing the required instances where needed. In practice, the appropriateness of a singleton depends on the context, the language features available, and the impact on testability and maintainability.

Outside programming, the term remains widely used to describe any entity that is the only one in a given context.