Pseudometric
A pseudometric is a mathematical concept used in the field of metric space theory. It is similar to a metric but does not require the distance between two points to be zero only when the points are identical. In other words, a pseudometric allows for the possibility that distinct points can have a distance of zero, which can be useful in certain applications.
Pseudometrics satisfy most of the properties of a metric, such as non-negativity, symmetry, and the triangle inequality. However, since they do not enforce the uniqueness of points based on distance, they are often used in areas like topology and functional analysis to study spaces where equivalence classes are important.