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E8

[0YV] In the exercise [0YS] it is important to require that the balls are centered in points of \(K\). Find an example of metric space \((X,d)\) and compact \(KβŠ† X\) of finite dimension, but such that, for every \(nβˆˆβ„•\) and every \(𝜌{\gt}0\), there are infinite disjoint balls each containing only one point of \(K\).

Solution 1

[0YW]

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