"quotient map" meaning in English

{
  "forms": [
    {
      "form": "quotient maps",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "quotient map (plural quotient maps)",
      "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": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "If the square [0,1]×[0,1] (with the subspace topology) in ℝ² (with the standard topology) is mapped onto the set [0,1)×[0,1) with the quotient map f(x,y)=(⌊x⌋,⌊y⌋), then the target space (with its induced quotient topology) is topologically equivalent to a torus."
        }
      ],
      "glosses": [
        "A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space."
      ],
      "id": "en-quotient_map-en-noun-PovNuBkC",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "surjective",
          "surjective"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "inverse image",
          "inverse image"
        ]
      ],
      "raw_glosses": [
        "(topology) A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space."
      ],
      "related": [
        {
          "word": "quotient space"
        },
        {
          "word": "quotient topology"
        }
      ],
      "synonyms": [
        {
          "word": "identification map"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "quotient map"
      ]
    }
  ],
  "word": "quotient map"
}

{
  "forms": [
    {
      "form": "quotient maps",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "quotient map (plural quotient maps)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "quotient space"
    },
    {
      "word": "quotient topology"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Topology"
      ],
      "examples": [
        {
          "text": "If the square [0,1]×[0,1] (with the subspace topology) in ℝ² (with the standard topology) is mapped onto the set [0,1)×[0,1) with the quotient map f(x,y)=(⌊x⌋,⌊y⌋), then the target space (with its induced quotient topology) is topologically equivalent to a torus."
        }
      ],
      "glosses": [
        "A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "surjective",
          "surjective"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "inverse image",
          "inverse image"
        ]
      ],
      "raw_glosses": [
        "(topology) A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "quotient map"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "identification map"
    }
  ],
  "word": "quotient map"
}