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单词 UltrametricSpace
释义

ultrametric space


The metric space  (X,d)  is called an ultrametric space, if its metric d is an ultrametric, i.e. if

d(x,z)max{d(x,y),d(y,z)}x,y,zX.

Example.  The field together with any of its p-adic metrics

dp(x,y)=|x-y|p,

where  ||p  is the p-adic valuation (http://planetmath.org/PAdicValuation) of ,  forms an ultrametric space.

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更新时间:2025/5/4 5:17:00