"topological vector space" meaning in All languages combined

{
  "forms": [
    {
      "form": "topological vector spaces",
      "tags": [
        "plural"
      ]
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  ],
  "head_templates": [
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      "expansion": "topological vector space (plural topological vector spaces)",
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
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        }
      ],
      "glosses": [
        "A vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions."
      ],
      "id": "en-topological_vector_space-en-noun-ksRoGadp",
      "links": [
        [
          "functional analysis",
          "functional analysis"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "topological field",
          "topological field"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "real",
          "real numbers"
        ],
        [
          "complex numbers",
          "complex numbers"
        ],
        [
          "continuous function",
          "continuous function"
        ]
      ],
      "qualifier": "functional analysis",
      "raw_glosses": [
        "(functional analysis) A vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions."
      ],
      "synonyms": [
        {
          "sense": "vector space with topology such that addition and scalar multiplication are continuous",
          "word": "linear topological space"
        }
      ],
      "wikipedia": [
        "topological vector space"
      ]
    }
  ],
  "word": "topological vector space"
}

{
  "forms": [
    {
      "form": "topological vector spaces",
      "tags": [
        "plural"
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  ],
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  "lang_code": "en",
  "pos": "noun",
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    {
      "categories": [
        "English countable nouns",
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      ],
      "glosses": [
        "A vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions."
      ],
      "links": [
        [
          "functional analysis",
          "functional analysis"
        ],
        [
          "vector space",
          "vector space"
        ],
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          "topological field"
        ],
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          "complex numbers",
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        ],
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      "qualifier": "functional analysis",
      "raw_glosses": [
        "(functional analysis) A vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions."
      ],
      "wikipedia": [
        "topological vector space"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "vector space with topology such that addition and scalar multiplication are continuous",
      "word": "linear topological space"
    }
  ],
  "word": "topological vector space"
}