"closure operator" meaning in English

{
  "forms": [
    {
      "form": "closure operators",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "closure operator (plural closure operators)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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          "kind": "other",
          "name": "English entries with incorrect language header",
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          "name": "Algebra",
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          "name": "Topology",
          "orig": "en:Topology",
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        }
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      "examples": [
        {
          "text": "1997 [Kluwer Academic], R. Friĉ, History of Sequential Convergence Spaces, C. E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 1, Springer, page 346,\nLet u be a closure operator on X satisfying the first three closure axioms: u(U∪B)=uU∪uB,A⊂u(A),u empty = empty ."
        }
      ],
      "glosses": [
        "A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure)."
      ],
      "hyponyms": [
        {
          "word": "algebraic closure operator"
        },
        {
          "word": "topological closure operator"
        }
      ],
      "id": "en-closure_operator-en-noun-wwRTQHXL",
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          "mathematics",
          "mathematics"
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          "topology",
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        [
          "algebra",
          "algebra"
        ],
        [
          "function",
          "function"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "closure",
          "closure"
        ]
      ],
      "qualifier": "\"on\" a set S",
      "raw_glosses": [
        "(mathematics, topology, algebra, \"on\" a set S) A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure)."
      ],
      "related": [
        {
          "word": "closure axiom"
        },
        {
          "word": "closure space"
        },
        {
          "word": "closure system"
        }
      ],
      "synonyms": [
        {
          "word": "hull operator"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "closure operator"
      ]
    }
  ],
  "word": "closure operator"
}

{
  "forms": [
    {
      "form": "closure operators",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "closure operator (plural closure operators)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "algebraic closure operator"
    },
    {
      "word": "topological closure operator"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "closure axiom"
    },
    {
      "word": "closure space"
    },
    {
      "word": "closure system"
    }
  ],
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        "en:Algebra",
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        "en:Topology"
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      "examples": [
        {
          "text": "1997 [Kluwer Academic], R. Friĉ, History of Sequential Convergence Spaces, C. E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 1, Springer, page 346,\nLet u be a closure operator on X satisfying the first three closure axioms: u(U∪B)=uU∪uB,A⊂u(A),u empty = empty ."
        }
      ],
      "glosses": [
        "A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure)."
      ],
      "links": [
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          "mathematics",
          "mathematics"
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          "topology",
          "topology"
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          "algebra",
          "algebra"
        ],
        [
          "function",
          "function"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "closure",
          "closure"
        ]
      ],
      "qualifier": "\"on\" a set S",
      "raw_glosses": [
        "(mathematics, topology, algebra, \"on\" a set S) A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure)."
      ],
      "synonyms": [
        {
          "word": "hull operator"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "closure operator"
      ]
    }
  ],
  "word": "closure operator"
}