Doubling Space

(Metric Geometry)

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sciences
Metric Geometry
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What is Doubling space?

In mathematics, a metric space X with metric d is said to be doubling if there is some doubling constant M > 0 such that for any x ∈ X and r > 0, it is possible to cover the ball B(x, r) = {y | d(x, y) < r} with the union of at most M balls of radius r/2. The base-2 logarithm of M is often referred to as the doubling dimension of X. Euclidean spaces ℝd equipped with the usual Euclidean metric are examples of doubling spaces where the doubling constant M depends on the dimension d. For example, in one dimension, M = 2; and in two dimensions, M = 7.

Technology Types

metric geometry

Synonyms

Doubling dimensionDoubling measureDoubling measuresDoubling Measures and Metric SpacesDoubling metric space

Translations

Свойство удвоения (ru)加倍空間 (zh)

Tech Info


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