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单词 PseudometricSpace
释义

pseudometric space


A pseudometric space is a set X together with a non-negative real-valued function d:X×X (called a pseudometric) such that, for every x,y,zX,

  • d(x,x)=0.

  • d(x,y)=d(y,x)

  • d(x,z)d(x,y)+d(y,z)

In other words, a pseudometric space is a generalizationPlanetmathPlanetmath of a metric space in which we allow the possibility that d(x,y)=0 for distinct values of x and y.

References

  • 1 L.A. Steen, J.A.Seebach, Jr.,Counterexamples in topology,Holt, Rinehart and Winston, Inc., 1970.
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更新时间:2025/5/4 16:40:52