"discrete topology" meaning in All languages combined

See discrete topology on Wiktionary

Noun [English]

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

{
  "forms": [
    {
      "form": "discrete topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "discrete topology (plural discrete topologies)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
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        },
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        },
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          "kind": "other",
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        },
        {
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
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        },
        {
          "kind": "other",
          "name": "Terms with Icelandic translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Mandarin translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "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",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "set",
          "set"
        ],
        [
          "subset",
          "subset"
        ]
      ],
      "raw_glosses": [
        "(topology) A topology on a set consisting of all subsets of that set."
      ],
      "related": [
        {
          "word": "discrete metric"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "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"
}
{
  "forms": [
    {
      "form": "discrete topologies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "discrete topology (plural discrete topologies)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "discrete metric"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with usage examples",
        "Entries with translation boxes",
        "Pages with 1 entry",
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        "Terms with Finnish translations",
        "Terms with Icelandic translations",
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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."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "set",
          "set"
        ],
        [
          "subset",
          "subset"
        ]
      ],
      "raw_glosses": [
        "(topology) A topology on a set consisting of all subsets of that set."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "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 All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-01 from the enwiktionary dump dated 2024-11-21 using wiktextract (95d2be1 and 64224ec). 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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