"discrete topology" meaning in English

See discrete topology in All languages combined, or Wiktionary

Noun

Forms: discrete topologies [plural]
Head templates: {{en-noun}} discrete topology (plural discrete topologies)
  1. (topology) A topology on a set consisting of all subsets of that set. Categories (topical): Topology Related terms: discrete metric Translations (topology on a set consisting of all subsets of that set): 離散拓撲 (Chinese Mandarin), 离散拓扑 (lísàn tuòpū) (Chinese Mandarin), diskreetti topologia (Finnish), sundurlaust grannmynstur [neuter] (Icelandic), strjált grannmynstur [neuter] (Icelandic)

Inflected forms

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    {
      "form": "discrete topologies",
      "tags": [
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  "lang_code": "en",
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  "senses": [
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      "examples": [
        {
          "text": "In the discrete topology all sets are open (but they are also all closed).",
          "type": "example"
        },
        {
          "text": "An infinite set with discrete topology is not compact.",
          "type": "example"
        }
      ],
      "glosses": [
        "A topology on a set consisting of all subsets of that set."
      ],
      "id": "en-discrete_topology-en-noun-teXXsQaB",
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          "set"
        ],
        [
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      ],
      "raw_glosses": [
        "(topology) A topology on a set consisting of all subsets of that set."
      ],
      "related": [
        {
          "word": "discrete metric"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
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      "translations": [
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "sense": "topology on a set consisting of all subsets of that set",
          "word": "離散拓撲"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "lísàn tuòpū",
          "sense": "topology on a set consisting of all subsets of that set",
          "word": "离散拓扑"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "topology on a set consisting of all subsets of that set",
          "word": "diskreetti topologia"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "topology on a set consisting of all subsets of that set",
          "tags": [
            "neuter"
          ],
          "word": "sundurlaust grannmynstur"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "topology on a set consisting of all subsets of that set",
          "tags": [
            "neuter"
          ],
          "word": "strjált grannmynstur"
        }
      ]
    }
  ],
  "word": "discrete topology"
}
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        {
          "text": "In the discrete topology all sets are open (but they are also all closed).",
          "type": "example"
        },
        {
          "text": "An infinite set with discrete topology is not compact.",
          "type": "example"
        }
      ],
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        "A topology on a set consisting of all subsets of that set."
      ],
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        "(topology) A topology on a set consisting of all subsets of that set."
      ],
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        "mathematics",
        "sciences",
        "topology"
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  "translations": [
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "topology on a set consisting of all subsets of that set",
      "word": "離散拓撲"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "lísàn tuòpū",
      "sense": "topology on a set consisting of all subsets of that set",
      "word": "离散拓扑"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "topology on a set consisting of all subsets of that set",
      "word": "diskreetti topologia"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "topology on a set consisting of all subsets of that set",
      "tags": [
        "neuter"
      ],
      "word": "sundurlaust grannmynstur"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "topology on a set consisting of all subsets of that set",
      "tags": [
        "neuter"
      ],
      "word": "strjált grannmynstur"
    }
  ],
  "word": "discrete topology"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.

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