"final topology" meaning in All languages combined

{
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    {
      "form": "final topologies",
      "tags": [
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      "expansion": "final topology (plural final topologies)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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            "Formal sciences",
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      "coordinate_terms": [
        {
          "word": "initial topology"
        }
      ],
      "glosses": [
        "Given a set X, a family of topological spaces (M#x5F;i,T#x5F;i)#x5F;#x7B;i#x5C;inI#x7D; and a family of functions f#x5F;i#x3A;M#x5F;i#x5C;toX, the final topology is the finest topology on X such that all f#x5F;i are continuous."
      ],
      "hyponyms": [
        {
          "word": "quotient topology"
        }
      ],
      "id": "en-final_topology-en-noun-ZOr7gQGi",
      "links": [
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          "topology",
          "topology"
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          "topological space",
          "topological space#English"
        ]
      ],
      "raw_glosses": [
        "(topology) Given a set X, a family of topological spaces (M#x5F;i,T#x5F;i)#x5F;#x7B;i#x5C;inI#x7D; and a family of functions f#x5F;i#x3A;M#x5F;i#x5C;toX, the final topology is the finest topology on X such that all f#x5F;i are continuous."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
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    }
  ],
  "word": "final topology"
}

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    {
      "word": "initial topology"
    }
  ],
  "forms": [
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      "form": "final topologies",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "topology",
          "topology"
        ],
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          "topological space",
          "topological space#English"
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      "raw_glosses": [
        "(topology) Given a set X, a family of topological spaces (M#x5F;i,T#x5F;i)#x5F;#x7B;i#x5C;inI#x7D; and a family of functions f#x5F;i#x3A;M#x5F;i#x5C;toX, the final topology is the finest topology on X such that all f#x5F;i are continuous."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "final topology"
}

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  "path": [
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  "section": "English",
  "subsection": "noun",
  "title": "final topology",
  "trace": ""
}