"algebraic topology" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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        {
          "text": "The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).",
          "type": "example"
        },
        {
          "text": "Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.",
          "type": "example"
        },
        {
          "text": "1969, Emil Artin, Hel Braun, Introduction to Algebraic Topology, C. E. Merrill Publishing Company,\nProfessor Emil Artin lectured on algebraic topology during the winter semester of 1959–60."
        },
        {
          "ref": "2001, James F. Davis, Paul Kirk, Lecture Notes in Algebraic Topology, American Mathematical Society, page xii",
          "text": "The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology.",
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          "text": "2002, Allen Hatcher, Algebraic Topology, Cambridge University Press:",
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      "glosses": [
        "The branch of mathematics that uses tools from abstract algebra to study topological spaces."
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          "abstract algebra",
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        [
          "topological space",
          "topological space"
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      "raw_glosses": [
        "(mathematics) The branch of mathematics that uses tools from abstract algebra to study topological spaces."
      ],
      "related": [
        {
          "word": "algebraic geometry"
        },
        {
          "word": "differential topology"
        }
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          "sense": "branch of mathematics",
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          "word": "combinatorial topology"
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      "translations": [
        {
          "code": "hy",
          "lang": "Armenian",
          "roman": "hanrahašvakan topologia",
          "sense": "branch of mathematics",
          "word": "հանրահաշվական տոպոլոգիա"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "branch of mathematics",
          "word": "algebrallinen topologia"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "branch of mathematics",
          "tags": [
            "feminine"
          ],
          "word": "algebraische Topologie"
        },
        {
          "code": "el",
          "lang": "Greek",
          "roman": "algevrikí topología",
          "sense": "branch of mathematics",
          "tags": [
            "feminine"
          ],
          "word": "αλγεβρική τοπολογία"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "branch of mathematics",
          "tags": [
            "feminine"
          ],
          "word": "topologia algebrica"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "branch of mathematics",
          "tags": [
            "feminine"
          ],
          "word": "topologia algébrica"
        }
      ],
      "wikipedia": [
        "algebraic topology"
      ]
    }
  ],
  "word": "algebraic topology"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "algebraic geometry"
    },
    {
      "word": "differential topology"
    }
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      "examples": [
        {
          "text": "The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).",
          "type": "example"
        },
        {
          "text": "Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.",
          "type": "example"
        },
        {
          "text": "1969, Emil Artin, Hel Braun, Introduction to Algebraic Topology, C. E. Merrill Publishing Company,\nProfessor Emil Artin lectured on algebraic topology during the winter semester of 1959–60."
        },
        {
          "ref": "2001, James F. Davis, Paul Kirk, Lecture Notes in Algebraic Topology, American Mathematical Society, page xii",
          "text": "The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology.",
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        {
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      "glosses": [
        "The branch of mathematics that uses tools from abstract algebra to study topological spaces."
      ],
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          "abstract algebra",
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        ],
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          "topological space",
          "topological space"
        ]
      ],
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        "(mathematics) The branch of mathematics that uses tools from abstract algebra to study topological spaces."
      ],
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        "uncountable"
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      "topics": [
        "mathematics",
        "sciences"
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  "synonyms": [
    {
      "sense": "branch of mathematics",
      "tags": [
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      "word": "combinatorial topology"
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  "translations": [
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "hanrahašvakan topologia",
      "sense": "branch of mathematics",
      "word": "հանրահաշվական տոպոլոգիա"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "branch of mathematics",
      "word": "algebrallinen topologia"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "branch of mathematics",
      "tags": [
        "feminine"
      ],
      "word": "algebraische Topologie"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "algevrikí topología",
      "sense": "branch of mathematics",
      "tags": [
        "feminine"
      ],
      "word": "αλγεβρική τοπολογία"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "branch of mathematics",
      "tags": [
        "feminine"
      ],
      "word": "topologia algebrica"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "branch of mathematics",
      "tags": [
        "feminine"
      ],
      "word": "topologia algébrica"
    }
  ],
  "word": "algebraic topology"
}