Adjective
English Wikipedia has an article on:Pseudometric spaceWikipedia
pseudometric (not comparable)
(mathematics) Describing a generalization of a metric space in which the distance between two distinct points can be zero.
Note that the symmetric difference of two distinct sets can have measure zero; hence the pseudometric as defined above need not to be a true metric. Source: Internet
Indeed, as discussed above, such a uniformity can be defined by a single pseudometric, which is necessarily a metric if the space is Hausdorff. Source: Internet
Indeed, since a metric is a fortiori a pseudometric, the pseudometric definition furnishes M with a uniform structure. Source: Internet
Less trivially, it can be shown that a uniform structure that admits a countable fundamental system of entourages (and hence in particular a uniformity defined by a countable family of pseudometrics) can be defined by a single pseudometric. Source: Internet
Other examples include: * Every metric space is Tychonoff; every pseudometric space is completely regular. Source: Internet
Proof The following is a standard proof that a complete pseudometric space is a Baire space. Source: Internet