pseudometric space

A pseudometric space is a set $X$ together with a non-negative real-valued function $d:X\\times X\\longrightarrow\\mathbb{R}$ (called a pseudometric) such that, for every $x,y,z\\in X$ ,

•
$d(x,x)=0$ .
•
$d(x,y)=d(y,x)$
•
$d(x,z)\\leq d(x,y)+d(y,z)$

In other words, a pseudometric space is a generalization 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.

单词	PseudometricSpace
释义	pseudometric space A pseudometric space is a set $X$ together with a non-negative real-valued function $d:X\\times X\\longrightarrow\\mathbb{R}$ (called a pseudometric) such that, for every $x,y,z\\in X$ , • $d(x,x)=0$ . • $d(x,y)=d(y,x)$ • $d(x,z)\\leq d(x,y)+d(y,z)$ In other words, a pseudometric space is a generalization 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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