Closed-ball meaning

(analysis) A ball which contains its boundary, i.e., a ball which is a closed set.

In the set of 3-adic numbers, the closed ball of radius 1/3 "centered" at 1 is the set . This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g.. Then each of those balls partitions into exactly 3 smaller closed balls of radius 1/27, and the sub-partitioning can be continued indefinitely, in a fractal manner.

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