closed ball

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closed ball ‎(plural closed balls)

  1. (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  \{x | \exists n \in \mathbb{Z} . \, x = 3 n + 1 \} . This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g., \{x | \exists n \in \mathbb{Z} . \, x = 4 + 9 n \} . 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.