"lower set" meaning in English

{
  "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": "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",
        "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"
}