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Quasimetric space
In mathematics, a quasimetric space (M,d ) is a set M together with a function d : M × M -> R (called a quasimetric) which satisfies the following conditions:
- d(x, y) ≥ 0 (non-negativity)
- d(x, y) = 0 if and only if x = y (identity of indiscernibles)
- d(x, z) ≤ d(x, y) + d(y, z) (triangle inequality).
Thus, the concept of a quasimetric space generalizes the concept of a metric space by lifting the condition of symmetry.
If (M,d ) is a quasimetric space, a metric space (M,d' ) can be formed by taking
- d' (x, y) = (d(x, y) + d(y, x)) / 2 .
Last updated: 05-27-2005 22:25:47
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details