Wikipedia:
semimetric space
In mathematics, a semimetric space generalizes the concept of a metric space by not requiring the condition of satisfying the triangle inequality. Thus, a semimetric space is a special case of a prametric space, being defined by a symmetric, discernible prametric. Because of its symmetry properties, in translations of Russian texts, a semimetric is sometimes called a symmetric.
Definition
A semimetric space (M,d) is a set M together with a function 
(called a
semimetric) which satisfies the following conditions:
(non-negativity);
(identity of
indiscernibles);
(symmetry)
References
- A.V. Arkhangelskii, L.S.Pontryagin, General Topology I, (1990) Springer-Verlag, Berlin. ISBN 3-540-18178-4
- L.A. Steen, J.A.Seebach, Jr., Counterexamples in Topology, (1970) Holt, Rinehart and Winston, Inc..
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