See open set on Wiktionary
Download JSON data for open set meaning in All languages combined (5.4kB)
{
"forms": [
{
"form": "open sets",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "open set (plural open sets)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Topology",
"orig": "en:Topology",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"glosses": [
"Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary."
],
"id": "en-open_set-en-noun-9n9PwcqA",
"links": [
[
"topology",
"topology"
],
[
"set",
"set"
]
],
"raw_glosses": [
"(topology) Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Topology",
"orig": "en:Topology",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "35 53 11",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
}
],
"glosses": [
"A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set."
],
"holonyms": [
{
"_dis1": "32 68 0",
"word": "topology"
},
{
"_dis1": "32 68 0",
"word": "topological space"
}
],
"id": "en-open_set-en-noun-QxuhO3wi",
"links": [
[
"topology",
"topology"
],
[
"mathematical analysis",
"mathematical analysis"
],
[
"set",
"set"
],
[
"union",
"union"
],
[
"open ball",
"open ball"
],
[
"point",
"point"
]
],
"meronyms": [
{
"_dis1": "28 50 22",
"sense": "in metric spaces",
"word": "open ball"
}
],
"qualifier": "restricted to metric spaces",
"raw_glosses": [
"(topology, mathematical analysis, restricted to metric spaces) A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set."
],
"related": [
{
"_dis1": "32 68 0",
"word": "closed set"
}
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences",
"topology"
],
"translations": [
{
"_dis1": "37 50 13",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "the set of all interior points",
"word": "開集"
},
{
"_dis1": "37 50 13",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "kāijí",
"sense": "the set of all interior points",
"word": "开集"
},
{
"_dis1": "37 50 13",
"code": "nl",
"lang": "Dutch",
"sense": "the set of all interior points",
"tags": [
"feminine"
],
"word": "open verzameling"
},
{
"_dis1": "37 50 13",
"code": "fi",
"lang": "Finnish",
"sense": "the set of all interior points",
"word": "avoin joukko"
},
{
"_dis1": "37 50 13",
"code": "fr",
"lang": "French",
"sense": "the set of all interior points",
"tags": [
"masculine"
],
"word": "ouvert"
},
{
"_dis1": "37 50 13",
"code": "fr",
"lang": "French",
"sense": "the set of all interior points",
"tags": [
"masculine"
],
"word": "ensemble ouvert"
},
{
"_dis1": "37 50 13",
"code": "de",
"lang": "German",
"sense": "the set of all interior points",
"tags": [
"feminine"
],
"word": "offene Menge"
},
{
"_dis1": "37 50 13",
"code": "el",
"lang": "Greek",
"roman": "anoiktó sýnolo",
"sense": "the set of all interior points",
"tags": [
"neuter"
],
"word": "ανοικτό σύνολο"
},
{
"_dis1": "37 50 13",
"code": "he",
"lang": "Hebrew",
"roman": "kvutzá ptukhá",
"sense": "the set of all interior points",
"tags": [
"feminine"
],
"word": "קבוצה פתוחה"
},
{
"_dis1": "37 50 13",
"alt": "かいしゅうごう",
"code": "ja",
"lang": "Japanese",
"roman": "kaishūgō",
"sense": "the set of all interior points",
"word": "開集合"
},
{
"_dis1": "37 50 13",
"code": "mk",
"lang": "Macedonian",
"roman": "otvoreno množestvo",
"sense": "the set of all interior points",
"tags": [
"neuter"
],
"word": "отворено множество"
},
{
"_dis1": "37 50 13",
"code": "pl",
"lang": "Polish",
"sense": "the set of all interior points",
"tags": [
"masculine"
],
"word": "zbiór otwarty"
},
{
"_dis1": "37 50 13",
"code": "ru",
"lang": "Russian",
"roman": "otkrýtoje mnóžestvo",
"sense": "the set of all interior points",
"tags": [
"neuter"
],
"word": "откры́тое мно́жество"
},
{
"_dis1": "37 50 13",
"code": "sv",
"lang": "Swedish",
"sense": "the set of all interior points",
"tags": [
"common-gender"
],
"word": "öppen mängd"
}
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Topology",
"orig": "en:Topology",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"glosses": [
"Most generally, a member of the topology of a given topological space."
],
"id": "en-open_set-en-noun-k2E8Vs4G",
"links": [
[
"topology",
"topology"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(topology) Most generally, a member of the topology of a given topological space."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
}
],
"wikipedia": [
"open set"
],
"word": "open set"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns"
],
"forms": [
{
"form": "open sets",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "open set (plural open sets)",
"name": "en-noun"
}
],
"holonyms": [
{
"word": "topology"
},
{
"word": "topological space"
}
],
"lang": "English",
"lang_code": "en",
"meronyms": [
{
"sense": "in metric spaces",
"word": "open ball"
}
],
"pos": "noun",
"related": [
{
"word": "closed set"
}
],
"senses": [
{
"categories": [
"en:Topology"
],
"glosses": [
"Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary."
],
"links": [
[
"topology",
"topology"
],
[
"set",
"set"
]
],
"raw_glosses": [
"(topology) Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
},
{
"categories": [
"en:Mathematical analysis",
"en:Topology"
],
"glosses": [
"A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set."
],
"links": [
[
"topology",
"topology"
],
[
"mathematical analysis",
"mathematical analysis"
],
[
"set",
"set"
],
[
"union",
"union"
],
[
"open ball",
"open ball"
],
[
"point",
"point"
]
],
"qualifier": "restricted to metric spaces",
"raw_glosses": [
"(topology, mathematical analysis, restricted to metric spaces) A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences",
"topology"
]
},
{
"categories": [
"en:Topology"
],
"glosses": [
"Most generally, a member of the topology of a given topological space."
],
"links": [
[
"topology",
"topology"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(topology) Most generally, a member of the topology of a given topological space."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "the set of all interior points",
"word": "開集"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "kāijí",
"sense": "the set of all interior points",
"word": "开集"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "the set of all interior points",
"tags": [
"feminine"
],
"word": "open verzameling"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "the set of all interior points",
"word": "avoin joukko"
},
{
"code": "fr",
"lang": "French",
"sense": "the set of all interior points",
"tags": [
"masculine"
],
"word": "ouvert"
},
{
"code": "fr",
"lang": "French",
"sense": "the set of all interior points",
"tags": [
"masculine"
],
"word": "ensemble ouvert"
},
{
"code": "de",
"lang": "German",
"sense": "the set of all interior points",
"tags": [
"feminine"
],
"word": "offene Menge"
},
{
"code": "el",
"lang": "Greek",
"roman": "anoiktó sýnolo",
"sense": "the set of all interior points",
"tags": [
"neuter"
],
"word": "ανοικτό σύνολο"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "kvutzá ptukhá",
"sense": "the set of all interior points",
"tags": [
"feminine"
],
"word": "קבוצה פתוחה"
},
{
"alt": "かいしゅうごう",
"code": "ja",
"lang": "Japanese",
"roman": "kaishūgō",
"sense": "the set of all interior points",
"word": "開集合"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "otvoreno množestvo",
"sense": "the set of all interior points",
"tags": [
"neuter"
],
"word": "отворено множество"
},
{
"code": "pl",
"lang": "Polish",
"sense": "the set of all interior points",
"tags": [
"masculine"
],
"word": "zbiór otwarty"
},
{
"code": "ru",
"lang": "Russian",
"roman": "otkrýtoje mnóžestvo",
"sense": "the set of all interior points",
"tags": [
"neuter"
],
"word": "откры́тое мно́жество"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "the set of all interior points",
"tags": [
"common-gender"
],
"word": "öppen mängd"
}
],
"wikipedia": [
"open set"
],
"word": "open set"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-04-26 from the enwiktionary dump dated 2024-04-21 using wiktextract (93a6c53 and 21a9316). 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.