closed ball

English

closed ball (plural closed balls)

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

单词	closed ball
释义	closed ball English Noun closed ball (plural closed balls) (mathematical 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 ${\\displaystyle \\{x\|\\exists n\\in \\mathbb {Z} .\\,x=3n+1\\}}$ . This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g., ${\\displaystyle \\{x\|\\exists n\\in \\mathbb {Z} .\\,x=4+9n\\}}$ . 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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