"initial topology" meaning in All languages combined

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      "tags": [
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      "expansion": "initial topology (plural initial topologies)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      ],
      "coordinate_terms": [
        {
          "word": "final 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;X#x5C;toM#x5F;i, the initial topology is the coarsest topology on X such that all f#x5F;i are continuous."
      ],
      "hyponyms": [
        {
          "word": "product topology"
        }
      ],
      "id": "en-initial_topology-en-noun-Ax0uF36C",
      "links": [
        [
          "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;X#x5C;toM#x5F;i, the initial topology is the coarsest topology on X such that all f#x5F;i are continuous."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
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    }
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  "word": "initial topology"
}

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  "coordinate_terms": [
    {
      "word": "final topology"
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      "form": "initial topologies",
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      "expansion": "initial topology (plural initial topologies)",
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      "word": "product topology"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        "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;X#x5C;toM#x5F;i, the initial topology is the coarsest topology on X such that all f#x5F;i are continuous."
      ],
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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;X#x5C;toM#x5F;i, the initial topology is the coarsest topology on X such that all f#x5F;i are continuous."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
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    }
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  "word": "initial topology"
}

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