"underlying set" meaning in English

{
  "forms": [
    {
      "form": "underlying sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "underlying set (plural underlying sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A set of \"points\" upon which a topology is built, thereby yielding a topological space."
      ],
      "id": "en-underlying_set-en-noun-ySE6y8dk",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "topological space",
          "topological space"
        ]
      ],
      "raw_glosses": [
        "(topology) A set of \"points\" upon which a topology is built, thereby yielding a topological space."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "23 77",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "17 83",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "9 91",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "A set upon which some operations are defined, thereby yielding an algebraic structure."
      ],
      "id": "en-underlying_set-en-noun-2xo~U4qi",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ]
      ],
      "raw_glosses": [
        "(algebra) A set upon which some operations are defined, thereby yielding an algebraic structure."
      ],
      "synonyms": [
        {
          "_dis1": "41 59",
          "topics": [
            "algebra",
            "mathematics",
            "sciences"
          ],
          "word": "carrier set"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "underlying set"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "Pages with 1 entry",
    "Pages with entries"
  ],
  "forms": [
    {
      "form": "underlying sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "underlying set (plural underlying sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "en:Topology"
      ],
      "glosses": [
        "A set of \"points\" upon which a topology is built, thereby yielding a topological space."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "topological space",
          "topological space"
        ]
      ],
      "raw_glosses": [
        "(topology) A set of \"points\" upon which a topology is built, thereby yielding a topological space."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    },
    {
      "categories": [
        "en:Algebra"
      ],
      "glosses": [
        "A set upon which some operations are defined, thereby yielding an algebraic structure."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ]
      ],
      "raw_glosses": [
        "(algebra) A set upon which some operations are defined, thereby yielding an algebraic structure."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "word": "carrier set"
    }
  ],
  "word": "underlying set"
}