"lower set" meaning in English

See lower set in All languages combined, or Wiktionary

Noun

Forms: lower sets [plural]
Head templates: {{en-noun}} lower set (plural lower sets)
  1. (mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself. Wikipedia link: lower set Categories (topical): Mathematics
    Sense id: en-lower_set-en-noun-k9pNl21X Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: mathematics, order-theory, sciences

Inflected forms

{
  "antonyms": [
    {
      "word": "upper set"
    }
  ],
  "forms": [
    {
      "form": "lower sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "lower set (plural lower sets)",
      "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": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A subset of a poset which contains any descending chain which starts at any element of itself."
      ],
      "id": "en-lower_set-en-noun-k9pNl21X",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "poset",
          "poset"
        ],
        [
          "chain",
          "chain"
        ]
      ],
      "raw_glosses": [
        "(mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself."
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences"
      ],
      "wikipedia": [
        "lower set"
      ]
    }
  ],
  "word": "lower set"
}
{
  "antonyms": [
    {
      "word": "upper set"
    }
  ],
  "forms": [
    {
      "form": "lower sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "lower set (plural lower sets)",
      "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",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "A subset of a poset which contains any descending chain which starts at any element of itself."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "poset",
          "poset"
        ],
        [
          "chain",
          "chain"
        ]
      ],
      "raw_glosses": [
        "(mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself."
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences"
      ],
      "wikipedia": [
        "lower set"
      ]
    }
  ],
  "word": "lower set"
}

Download raw JSONL data for lower set meaning in English (0.9kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.