"product topology" meaning in English

{
  "forms": [
    {
      "form": "product topologies",
      "tags": [
        "plural"
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  ],
  "head_templates": [
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      "expansion": "product topology (plural product topologies)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "name": "English entries with incorrect language header",
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          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
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      ],
      "glosses": [
        "The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper."
      ],
      "id": "en-product_topology-en-noun-tv75sEOD",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "Cartesian product",
          "Cartesian product"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "basis",
          "basis"
        ],
        [
          "open",
          "open set"
        ],
        [
          "proper",
          "proper subset"
        ]
      ],
      "raw_glosses": [
        "(topology) The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper."
      ],
      "related": [
        {
          "word": "box topology"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "product topology"
}

{
  "forms": [
    {
      "form": "product topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "product topology (plural product topologies)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "box topology"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
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      ],
      "glosses": [
        "The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "Cartesian product",
          "Cartesian product"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "basis",
          "basis"
        ],
        [
          "open",
          "open set"
        ],
        [
          "proper",
          "proper subset"
        ]
      ],
      "raw_glosses": [
        "(topology) The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "product topology"
}