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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 the category Rel of sets and relations, the empty set is the unique initial object, the unique terminal object, and hence the unique zero object. Morphisms of pointed sets.
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 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.
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.
All fields are left at their initial value of 0 (integer types), 0.0 (floating-point types), false (boolean type), or null (reference types). A programmer-defined constructor that takes no parameters is also called a default constructor in C#, but not in Java. [4] [5]
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The empty set is finite, as it can be enumerated by means of the empty initial segment of the natural numbers. The term enumerable set is sometimes used for countable sets. However it is also often used for computably enumerable sets , which are the countable sets for which an enumeration function can be computed with an algorithm.