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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 class null is a subclass of the symbol class, because nil is a symbol. Since nil also represents the empty list, null is a subclass of the list class, too. Methods parameters specialized to symbol or list will thus take a nil argument. Of course, a null specialization can still be defined which is a more specific match for nil.
[1] [2] It is used in varying context from "having zero members in a set" (e.g., null set) [3] to "having a value of zero" (e.g., null vector). [4] In a vector space, the null vector is the neutral element of vector addition; depending on the context, a null vector may also be a vector mapped to some null by a function under consideration (such ...
Null sets play a key role in the definition of the Lebesgue integral: if functions and are equal except on a null set, then is integrable if and only if is, and their integrals are equal. This motivates the formal definition of L p {\displaystyle L^{p}} spaces as sets of equivalence classes of functions which differ only on null sets.
The left null space of A is the same as the kernel of A T. The left null space of A is the orthogonal complement to the column space of A, and is dual to the cokernel of the associated linear transformation. The kernel, the row space, the column space, and the left null space of A are the four fundamental subspaces associated with the matrix A.
Nullable types are a feature of some programming languages which allow a value to be set to the special value NULL instead of the usual possible values of the data type.In statically typed languages, a nullable type is an option type, [citation needed] while in dynamically typed languages (where values have types, but variables do not), equivalent behavior is provided by having a single null ...
Even a string of length zero can require memory to store it, depending on the format being used. In most programming languages, the empty string is distinct from a null reference (or null pointer) because a null reference points to no string at all, not even the empty string. The empty string is a legitimate string, upon which most string ...
It follows that the null space of A is the orthogonal complement to the row space. For example, if the row space is a plane through the origin in three dimensions, then the null space will be the perpendicular line through the origin. This provides a proof of the rank–nullity theorem (see dimension above).