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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 length of a string is found by searching for the (first) NUL. This can be slow as it takes O(n) (linear time) with respect to the string length. It also means that a string cannot contain a NUL (there is a NUL in memory, but it is after the last character, not in the string).
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.
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 ...
This means a string cannot contain the zero code unit, as the first one seen marks the end of the string. The length of a string is the number of code units before the zero code unit. [1] The memory occupied by a string is always one more code unit than the length, as space is needed to store the zero terminator.
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
The ability to represent a null character does not always mean the resulting string will be correctly interpreted, as many programs will consider the null to be the end of the string. Thus the ability to type it (in case of unchecked user input) creates a vulnerability known as null byte injection and can lead to security exploits. [10]
By returning a null object (i.e., an empty list) instead, there is no need to verify that the return value is in fact a list. The calling function may simply iterate the list as normal, effectively doing nothing. It is, however, still possible to check whether the return value is a null object (an empty list) and react differently if desired.