"quotient space" meaning in English

{
  "forms": [
    {
      "form": "quotient spaces",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "quotient space (plural quotient spaces)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
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          "source": "w"
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          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
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            "Formal sciences",
            "Sciences",
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
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      "examples": [
        {
          "ref": "1983, K. D. Joshi, Introduction to General Topology, New Age International, page 129",
          "text": "Thus if #x5C;mathfrak#x7B;D#x7D; is an arbitrary decomposition of a space X into mutually disjoint subsets, then the corresponding quotient space is obtained by 'shrinking' or 'identifying' each member of #x5C;mathfrak#x7B;D#x7D; to a single point. For this reason, the quotient spaces are sometimes called identification spaces and quotient maps as identification maps.",
          "type": "quotation"
        },
        {
          "text": "1989, unnamed translator, Nicolas Bourbaki, Elements of Mathematics: General Topology: Chapters 1-4, [1971, N. Bourbaki, Éléments de Mathématique: Topologie Générale 1-4, Masson], Springer, page 110,\nPROPOSITION 6. Every quotient space of a connected space is connected."
        },
        {
          "ref": "2004, Silvia Biasotti, Bianca Falcidieno, Michela Spagnuolo, “6: Surface Shape Understanding Based on Extended Reeb Graphs”, in Sanjay Rana, editor, Topological Data Structures for Surfaces: An Introduction to Geographical Information Science, Wiley, page 96",
          "text": "The quotient space obtained from such a relation is called extended Reeb (ER) quotient space. Moreover, the ER quotient space, which is an abstract sub-space of M* and is independent from the geometry, may be represented as a traditional graph, which is called the extended Reeb graph (ERG).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A space obtained from another by identification of points that are equivalent to one another in some equivalence relation."
      ],
      "id": "en-quotient_space-en-noun-UY~i~J4n",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "identification",
          "identification"
        ],
        [
          "point",
          "point"
        ],
        [
          "equivalent",
          "equivalent"
        ],
        [
          "equivalence relation",
          "equivalence relation"
        ]
      ],
      "raw_glosses": [
        "(topology and algebra) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation."
      ],
      "related": [
        {
          "word": "quotient map"
        },
        {
          "word": "quotient topology"
        },
        {
          "word": "equivalence class"
        },
        {
          "topics": [
            "group-theory",
            "mathematics",
            "sciences"
          ],
          "word": "quotient group"
        }
      ],
      "synonyms": [
        {
          "sense": "space composed of points equivalent to each other in some relation",
          "word": "identification space"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "quotient space"
}

{
  "forms": [
    {
      "form": "quotient spaces",
      "tags": [
        "plural"
      ]
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  ],
  "head_templates": [
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      "expansion": "quotient space (plural quotient spaces)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "quotient map"
    },
    {
      "word": "quotient topology"
    },
    {
      "word": "equivalence class"
    },
    {
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "word": "quotient group"
    }
  ],
  "senses": [
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        "en:Algebra",
        "en:Topology"
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      "examples": [
        {
          "ref": "1983, K. D. Joshi, Introduction to General Topology, New Age International, page 129",
          "text": "Thus if #x5C;mathfrak#x7B;D#x7D; is an arbitrary decomposition of a space X into mutually disjoint subsets, then the corresponding quotient space is obtained by 'shrinking' or 'identifying' each member of #x5C;mathfrak#x7B;D#x7D; to a single point. For this reason, the quotient spaces are sometimes called identification spaces and quotient maps as identification maps.",
          "type": "quotation"
        },
        {
          "text": "1989, unnamed translator, Nicolas Bourbaki, Elements of Mathematics: General Topology: Chapters 1-4, [1971, N. Bourbaki, Éléments de Mathématique: Topologie Générale 1-4, Masson], Springer, page 110,\nPROPOSITION 6. Every quotient space of a connected space is connected."
        },
        {
          "ref": "2004, Silvia Biasotti, Bianca Falcidieno, Michela Spagnuolo, “6: Surface Shape Understanding Based on Extended Reeb Graphs”, in Sanjay Rana, editor, Topological Data Structures for Surfaces: An Introduction to Geographical Information Science, Wiley, page 96",
          "text": "The quotient space obtained from such a relation is called extended Reeb (ER) quotient space. Moreover, the ER quotient space, which is an abstract sub-space of M* and is independent from the geometry, may be represented as a traditional graph, which is called the extended Reeb graph (ERG).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A space obtained from another by identification of points that are equivalent to one another in some equivalence relation."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "identification",
          "identification"
        ],
        [
          "point",
          "point"
        ],
        [
          "equivalent",
          "equivalent"
        ],
        [
          "equivalence relation",
          "equivalence relation"
        ]
      ],
      "raw_glosses": [
        "(topology and algebra) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "space composed of points equivalent to each other in some relation",
      "word": "identification space"
    }
  ],
  "word": "quotient space"
}