 Because of this analogy the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis.When a topology is generated using a family of pseudometrics, the space is called a gauge space.A pseudometric space formula_1 is a set formula_2 together with a non-negative real-valued function formula_3 (called a pseudometric) such that,for every formula_4,

Unlike a metric space, points in a pseudometric space need not be distinguishable; that is, one may have formula_8 for distinct values formula_9.