"closed ball" meaning in English

{
  "forms": [
    {
      "form": "closed balls",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "closed ball (plural closed balls)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "In the set of 3-adic numbers, the closed ball of radius 1/3 \"centered\" at 1 is the set x|∃n∈ℤ.,x=3n+1. This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g., x|∃n∈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."
        }
      ],
      "glosses": [
        "A ball which contains its boundary, i.e., a ball which is a closed set."
      ],
      "id": "en-closed_ball-en-noun-g0v9JucX",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "ball",
          "ball"
        ],
        [
          "boundary",
          "boundary"
        ],
        [
          "closed set",
          "closed set"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A ball which contains its boundary, i.e., a ball which is a closed set."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "closed ball"
}

{
  "forms": [
    {
      "form": "closed balls",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "closed ball (plural closed balls)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "text": "In the set of 3-adic numbers, the closed ball of radius 1/3 \"centered\" at 1 is the set x|∃n∈ℤ.,x=3n+1. This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g., x|∃n∈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."
        }
      ],
      "glosses": [
        "A ball which contains its boundary, i.e., a ball which is a closed set."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "ball",
          "ball"
        ],
        [
          "boundary",
          "boundary"
        ],
        [
          "closed set",
          "closed set"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A ball which contains its boundary, i.e., a ball which is a closed set."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "closed ball"
}