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A class diagram exemplifying the singleton pattern.. In object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance.
A set such as {{,,}} is a singleton as it contains a single element (which itself is a set, but not a singleton). A set is a singleton if and only if its cardinality is 1. In von Neumann's set-theoretic construction of the natural numbers, the number 1 is defined as the singleton {}.
The empty set is the unique initial object in Set, the category of sets. Every one-element set ( singleton ) is a terminal object in this category; there are no zero objects. Similarly, the empty space is the unique initial object in Top , the category of topological spaces and every one-point space is a terminal object in this category.
The book was written by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides, with a foreword by Grady Booch. The book is divided into two parts, with the first two chapters exploring the capabilities and pitfalls of object-oriented programming, and the remaining chapters describing 23 classic software design patterns.
If D is the set of cards in a standard 52-card deck, the same-color-as relation on D – which can be denoted ~ C – has two equivalence classes: the sets {red cards} and {black cards}. The 2-part partition corresponding to ~ C has a refinement that yields the same-suit-as relation ~ S , which has the four equivalence classes {spades ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Whereas the singleton allows only one instance of a class to be created, the multiton pattern allows for the controlled creation of multiple instances, which it manages through the use of a map. Rather than having a single instance per application (e.g. the java.lang.Runtime object in the Java programming language ) the multiton pattern instead ...
The set of homeomorphism classes of compact surfaces with the connected sum. Its unit element is the class of the ordinary 2-sphere. Its unit element is the class of the ordinary 2-sphere. Furthermore, if a denotes the class of the torus , and b denotes the class of the projective plane, then every element c of the monoid has a unique ...