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The empty set is the unique initial object in Set, the category of sets. Every one-element set 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.
In computer programming, lazy initialization is the tactic of delaying the creation of an object, the calculation of a value, or some other expensive process until the first time it is needed.
In object-oriented computer programming, a null object is an object with no referenced value or with defined neutral (null) behavior.The null object design pattern, which describes the uses of such objects and their behavior (or lack thereof), was first published as "Void Value" [1] and later in the Pattern Languages of Program Design book series as "Null Object".
The latter list is sometimes called the "initializer list" or "initialization list" (although the term "initializer list" is formally reserved for initialization of class/struct members in C++; see below). A declaration which creates a data object, instead of merely describing its existence, is commonly called a definition.
The empty set serves as the initial object in Set with empty functions as morphisms. Every singleton is a terminal object, with the functions mapping all elements of the source sets to the single target element as morphisms. There are thus no zero objects in Set. The category Set is complete and co-complete.
When an array of objects is declared, e.g. MyClass x[10];; or allocated dynamically, e.g. new MyClass [10]. The default constructor of MyClass is used to initialize all the elements. When a derived class constructor does not explicitly call the base class constructor in its initializer list, the default constructor for the base class is called.
The empty set (considered as a preordered set) is the initial object of Ord, and the terminal objects are precisely the singleton preordered sets.
The empty set can be turned into a topological space, called the empty space, in just one way: by defining the empty set to be open. This empty topological space is the unique initial object in the category of topological spaces with continuous maps. In fact, it is a strict initial object: only the empty set has a function to the empty set.