In mathematics, a pseudometric space is a generalized metric space in which the distance between two distinct points can be zero. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. 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.
Read more about Pseudometric Space: Definition, Examples, Topology, Metric Identification
Famous quotes containing the word space:
“This moment exhibits infinite space, but there is a space also wherein all moments are infinitely exhibited, and the everlasting duration of infinite space is another region and room of joys.”
—Thomas Traherne (1636–1674)