"principal ultrafilter" meaning in English

{
  "antonyms": [
    {
      "word": "free ultrafilter"
    }
  ],
  "forms": [
    {
      "form": "principal ultrafilters",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "principal ultrafilter (plural principal ultrafilters)",
      "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"
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          "source": "w"
        },
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          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An ultrafilter such that every set belonging to it is the superset of some fixed singleton set."
      ],
      "hypernyms": [
        {
          "word": "principal filter"
        },
        {
          "word": "ultrafilter"
        }
      ],
      "id": "en-principal_ultrafilter-en-noun-Z6nZ43k3",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "ultrafilter",
          "ultrafilter"
        ],
        [
          "superset",
          "superset"
        ],
        [
          "singleton",
          "singleton"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An ultrafilter such that every set belonging to it is the superset of some fixed singleton set."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "principal ultrafilter"
}

{
  "antonyms": [
    {
      "word": "free ultrafilter"
    }
  ],
  "forms": [
    {
      "form": "principal ultrafilters",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "principal ultrafilter (plural principal ultrafilters)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "principal filter"
    },
    {
      "word": "ultrafilter"
    }
  ],
  "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",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "An ultrafilter such that every set belonging to it is the superset of some fixed singleton set."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "ultrafilter",
          "ultrafilter"
        ],
        [
          "superset",
          "superset"
        ],
        [
          "singleton",
          "singleton"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An ultrafilter such that every set belonging to it is the superset of some fixed singleton set."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "principal ultrafilter"
}