"topological space" meaning in English

See topological space in All languages combined, or Wiktionary

Noun

Forms: topological spaces [plural]
Head templates: {{en-noun}} topological space (plural topological spaces)
  1. (topology, formally) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets); Tags: formal Categories (topical): Topology
    Sense id: en-topological_space-en-noun-Q542B8kx Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 47 53 Disambiguation of Pages with 1 entry: 46 54 Disambiguation of Pages with entries: 45 55 Topics: mathematics, sciences, topology
  2. (topology, formally) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets); Tags: broadly, formal Categories (topical): Topology Hypernyms: mathematical space, space Hyponyms: normal space, pointed space, regular space, suspension Hyponyms (sober space): Hausdorff space Hyponyms (uniform space): metric space Meronyms: topology, open set, underlying set Translations (set that has a topology): 拓扑空间 (tuòpū kōngjiān) (Chinese Mandarin), topologisk rum [neuter] (Danish), topologinen avaruus (Finnish), espazo topolóxico [masculine] (Galician), τοπολογικός χώρος (topologikós chóros) [masculine] (Greek), spazio topologico [masculine] (Italian), topologiskt rum (Swedish)
    Sense id: en-topological_space-en-noun-akpPmCYj Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Afrikaans translations, Terms with Czech translations, Terms with Danish translations, Terms with Finnish translations, Terms with French translations, Terms with Galician translations, Terms with German translations, Terms with Greek translations, Terms with Hebrew translations, Terms with Icelandic translations, Terms with Italian translations, Terms with Japanese translations, Terms with Mandarin translations, Terms with Portuguese translations, Terms with Romanian translations, Terms with Russian translations, Terms with Serbo-Croatian translations, Terms with Spanish translations, Terms with Swedish translations, Topological spaces Disambiguation of English entries with incorrect language header: 47 53 Disambiguation of Entries with translation boxes: 30 70 Disambiguation of Pages with 1 entry: 46 54 Disambiguation of Pages with entries: 45 55 Disambiguation of Terms with Afrikaans translations: 39 61 Disambiguation of Terms with Czech translations: 39 61 Disambiguation of Terms with Danish translations: 34 66 Disambiguation of Terms with Finnish translations: 38 62 Disambiguation of Terms with French translations: 39 61 Disambiguation of Terms with Galician translations: 39 61 Disambiguation of Terms with German translations: 36 64 Disambiguation of Terms with Greek translations: 39 61 Disambiguation of Terms with Hebrew translations: 39 61 Disambiguation of Terms with Icelandic translations: 39 61 Disambiguation of Terms with Italian translations: 39 61 Disambiguation of Terms with Japanese translations: 39 61 Disambiguation of Terms with Mandarin translations: 40 60 Disambiguation of Terms with Portuguese translations: 41 59 Disambiguation of Terms with Romanian translations: 39 61 Disambiguation of Terms with Russian translations: 39 61 Disambiguation of Terms with Serbo-Croatian translations: 39 61 Disambiguation of Terms with Spanish translations: 40 60 Disambiguation of Terms with Swedish translations: 39 61 Disambiguation of Topological spaces: 36 64 Topics: mathematics, sciences, topology Disambiguation of 'sober space': 35 65 Disambiguation of 'uniform space': 36 64 Disambiguation of 'set that has a topology': 40 60
The following are not (yet) sense-disambiguated
Translations (ordered pair of a set and its topology): topologiese ruimte (Afrikaans), 拓扑空间 (tuòpū kōngjiān) (Chinese Mandarin), topologisk rum [neuter] (Danish), topologinen avaruus (Finnish), espace topologique [feminine] (French), espazo tipolóxico [masculine] (Galician), topologischer Raum [masculine] (German), τοπολογικός χώρος (topologikós chóros) [masculine] (Greek), מרחב טופולוגי (mercháv topológi) [masculine] (Hebrew), grannrúm [neuter] (Icelandic), spazio topologico [masculine] (Italian), 位相空間 (isō kūkan) (alt: いそう くうかん) (Japanese), espaço topológico [masculine] (Portuguese), spațiu topologic [neuter] (Romanian), топологи́ческое простра́нство (topologíčeskoje prostránstvo) [neuter] (Russian), espacio topológico [masculine] (Spanish), topologiskt rum (Swedish)
Disambiguation of 'ordered pair of a set and its topology': 50 50

Inflected forms

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      "word": "topologiese ruimte"
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      "word": "espace topologique"
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      "word": "topologischer Raum"
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      "word": "τοπολογικός χώρος"
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      "code": "he",
      "lang": "Hebrew",
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      "sense": "ordered pair of a set and its topology",
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      "code": "is",
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      "_dis1": "50 50",
      "alt": "いそう くうかん",
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      "sense": "ordered pair of a set and its topology",
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      "sense": "ordered pair of a set and its topology",
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        "neuter"
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          "topology"
        ],
        [
          "ordered pair",
          "ordered pair"
        ],
        [
          "set",
          "set"
        ],
        [
          "open set",
          "open set"
        ],
        [
          "closed set",
          "closed set"
        ]
      ],
      "raw_glosses": [
        "(topology, formally) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);"
      ],
      "tags": [
        "formal"
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "en:Topology"
      ],
      "glosses": [
        "An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);\n(loosely) the set X.",
        "the set X."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "ordered pair",
          "ordered pair"
        ],
        [
          "set",
          "set"
        ],
        [
          "open set",
          "open set"
        ],
        [
          "closed set",
          "closed set"
        ]
      ],
      "raw_glosses": [
        "(topology, formally) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);"
      ],
      "tags": [
        "broadly",
        "formal"
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "translations": [
    {
      "code": "af",
      "lang": "Afrikaans",
      "sense": "ordered pair of a set and its topology",
      "word": "topologiese ruimte"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "tuòpū kōngjiān",
      "sense": "ordered pair of a set and its topology",
      "word": "拓扑空间"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "neuter"
      ],
      "word": "topologisk rum"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "ordered pair of a set and its topology",
      "word": "topologinen avaruus"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "feminine"
      ],
      "word": "espace topologique"
    },
    {
      "code": "gl",
      "lang": "Galician",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "espazo tipolóxico"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "topologischer Raum"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "topologikós chóros",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "τοπολογικός χώρος"
    },
    {
      "code": "he",
      "lang": "Hebrew",
      "roman": "mercháv topológi",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "מרחב טופולוגי"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "neuter"
      ],
      "word": "grannrúm"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "spazio topologico"
    },
    {
      "alt": "いそう くうかん",
      "code": "ja",
      "lang": "Japanese",
      "roman": "isō kūkan",
      "sense": "ordered pair of a set and its topology",
      "word": "位相空間"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "espaço topológico"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "neuter"
      ],
      "word": "spațiu topologic"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "topologíčeskoje prostránstvo",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "neuter"
      ],
      "word": "топологи́ческое простра́нство"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "ordered pair of a set and its topology",
      "tags": [
        "masculine"
      ],
      "word": "espacio topológico"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "ordered pair of a set and its topology",
      "word": "topologiskt rum"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "tuòpū kōngjiān",
      "sense": "set that has a topology",
      "word": "拓扑空间"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "set that has a topology",
      "tags": [
        "neuter"
      ],
      "word": "topologisk rum"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "set that has a topology",
      "word": "topologinen avaruus"
    },
    {
      "code": "gl",
      "lang": "Galician",
      "sense": "set that has a topology",
      "tags": [
        "masculine"
      ],
      "word": "espazo topolóxico"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "topologikós chóros",
      "sense": "set that has a topology",
      "tags": [
        "masculine"
      ],
      "word": "τοπολογικός χώρος"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "set that has a topology",
      "tags": [
        "masculine"
      ],
      "word": "spazio topologico"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "set that has a topology",
      "word": "topologiskt rum"
    }
  ],
  "wikipedia": [
    "topological space"
  ],
  "word": "topological space"
}

Download raw JSONL data for topological space meaning in English (7.9kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.