Ultrametric distance

In Topology, a ultrametric distance is a Distance D on a unit X checking the inequality ultratriangulaire:

$d\; (X,\; Z)\; \backslash \; Leq\; \backslash \; max\; (D\; (X,\; there),\; D\; (there,\; Z))$. Important examples intervene in p-adic analysis.

Properties

• In a Space ultrametric, the closed Ball of center X and ray not no one R is open. The open Ball of center X and ray not no one R one is closed.

• Any point of a ball (opened or closed) is its center.

• All Triangle is isosceles.

Examples

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