"free ultrafilter" meaning in English

{
  "antonyms": [
    {
      "word": "principal ultrafilter"
    }
  ],
  "forms": [
    {
      "form": "free ultrafilters",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "free ultrafilter (plural free 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"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
      ],
      "hypernyms": [
        {
          "word": "free filter"
        },
        {
          "word": "ultrafilter"
        }
      ],
      "id": "en-free_ultrafilter-en-noun--liG2B-W",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "ultrafilter",
          "ultrafilter"
        ],
        [
          "cofinite",
          "cofinite"
        ]
      ],
      "qualifier": "especially nonstandard analysis",
      "raw_glosses": [
        "(mathematical analysis, especially nonstandard analysis) An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "free ultrafilter"
}

{
  "antonyms": [
    {
      "word": "principal ultrafilter"
    }
  ],
  "forms": [
    {
      "form": "free ultrafilters",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "free ultrafilter (plural free ultrafilters)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "free 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:Mathematical analysis"
      ],
      "glosses": [
        "An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "ultrafilter",
          "ultrafilter"
        ],
        [
          "cofinite",
          "cofinite"
        ]
      ],
      "qualifier": "especially nonstandard analysis",
      "raw_glosses": [
        "(mathematical analysis, especially nonstandard analysis) An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "free ultrafilter"
}