Ultrametric Space
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High Quality Content by WIKIPEDIA articles! In mathematics, an ultrametric space is a special kind of metric space in which the triangle inequality is replaced with d(x, z) max{d(x, y), d(y, z)}. Sometimes the associated metric is also called non-Archimedean metric or super-metric. Although some of the theorems for ultrametric spaces may seem strange at a first glance, they appear naturally in many applications. A contraction mapping may then be thought of as a way of approximating the final result of a computation (which can be guaranteed to exist by the Banach fixed point theorem). Similar i...
High Quality Content by WIKIPEDIA articles! In mathematics, an ultrametric space is a special kind of metric space in which the triangle inequality is replaced with d(x, z) max{d(x, y), d(y, z)}. Sometimes the associated metric is also called non-Archimedean metric or super-metric. Although some of the theorems for ultrametric spaces may seem strange at a first glance, they appear naturally in many applications. A contraction mapping may then be thought of as a way of approximating the final result of a computation (which can be guaranteed to exist by the Banach fixed point theorem). Similar ideas can be found in domain theory.
