Pseudometric Space - Definition

Definition

A pseudometric space is a set together with a non-negative real-valued function (called a pseudometric) such that, for every ,

  1. .
  2. (symmetry)
  3. (subadditivity/triangle inequality)

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

Read more about this topic:  Pseudometric Space

Famous quotes containing the word definition:

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.
    Elaine Heffner (20th century)

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)