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A class diagram exemplifying the singleton pattern. In object-oriented programming, ... The following Java 5+ example [6] is a thread-safe implementation, ...
In mathematics, a singleton (also known as a unit set [1] or one-point set) is a set with exactly one element. For example, the set { 0 } {\displaystyle \{0\}} is a singleton whose single element is 0 {\displaystyle 0} .
Singleton pattern, a design pattern that allows only one instance of a class to exist; Singleton bound, used in coding theory; Singleton variable, a variable that is referenced only once; Singleton, a character encoded with one unit in variable-width encoding schemes for computer character sets
In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets.In every topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only connected subsets.
If the space X is a metric space, for example a Euclidean space, then an element x of S is an isolated point of S if there exists an open ball around x that contains only finitely many elements of S. A point set that is made up only of isolated points is called a discrete set or discrete point set (see also discrete space).
A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences". Tuples are usually written by listing the elements within parentheses "( )" and separated by commas; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Other types of brackets are ...
In other words, it cannot be a fully conserved (i.e., invariable) site nor can it be a (singleton) site with a difference in only one sequence (as seen, for example, in single-nucleotide polymorphisms and single-nucleotide variants). In both cases, the number of character-state changes is the same regardless of the topology of the tree, equal ...
Likewise, there is a unique topology on a singleton set {a}. Here the open sets are ∅ and { a }. This topology is both discrete and trivial , although in some ways it is better to think of it as a discrete space since it shares more properties with the family of finite discrete spaces.