"distinguished open set" meaning in All languages combined

{
  "forms": [
    {
      "form": "distinguished open sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "distinguished open set (plural distinguished open 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": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
      ],
      "id": "en-distinguished_open_set-en-noun-1zlFDW5w",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "basic",
          "base"
        ],
        [
          "set",
          "set"
        ],
        [
          "generalizing",
          "generalize"
        ],
        [
          "compliment",
          "compliment"
        ],
        [
          "hypersurface",
          "hypersurface"
        ],
        [
          "algebraic varieties",
          "algebraic varieties"
        ],
        [
          "affine schemes",
          "affine schemes"
        ],
        [
          "projective",
          "projective variety"
        ],
        [
          "zero locus",
          "zero locus"
        ],
        [
          "affine",
          "affine space"
        ],
        [
          "projective",
          "projective space"
        ],
        [
          "scheme theory",
          "scheme theory"
        ],
        [
          "prime ideal",
          "prime ideal"
        ],
        [
          "commutative ring",
          "commutative ring"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "distinguished open set"
}

{
  "forms": [
    {
      "form": "distinguished open sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "distinguished open set (plural distinguished open 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:Algebraic geometry"
      ],
      "glosses": [
        "A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
      ],
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "basic",
          "base"
        ],
        [
          "set",
          "set"
        ],
        [
          "generalizing",
          "generalize"
        ],
        [
          "compliment",
          "compliment"
        ],
        [
          "hypersurface",
          "hypersurface"
        ],
        [
          "algebraic varieties",
          "algebraic varieties"
        ],
        [
          "affine schemes",
          "affine schemes"
        ],
        [
          "projective",
          "projective variety"
        ],
        [
          "zero locus",
          "zero locus"
        ],
        [
          "affine",
          "affine space"
        ],
        [
          "projective",
          "projective space"
        ],
        [
          "scheme theory",
          "scheme theory"
        ],
        [
          "prime ideal",
          "prime ideal"
        ],
        [
          "commutative ring",
          "commutative ring"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "distinguished open set"
}