See free ultrafilter on Wiktionary
{
"antonyms": [
{
"word": "principal ultrafilter"
}
],
"forms": [
{
"form": "free ultrafilters",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "free ultrafilter (plural free ultrafilters)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w"
},
{
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"parents": [],
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},
{
"kind": "other",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [],
"source": "w"
}
],
"glosses": [
"An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
],
"hypernyms": [
{
"word": "free filter"
},
{
"word": "ultrafilter"
}
],
"id": "en-free_ultrafilter-en-noun--liG2B-W",
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"ultrafilter",
"ultrafilter"
],
[
"cofinite",
"cofinite"
]
],
"qualifier": "especially nonstandard analysis",
"raw_glosses": [
"(mathematical analysis, especially nonstandard analysis) An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
}
],
"word": "free ultrafilter"
}
{
"antonyms": [
{
"word": "principal ultrafilter"
}
],
"forms": [
{
"form": "free ultrafilters",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "free ultrafilter (plural free ultrafilters)",
"name": "en-noun"
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"hypernyms": [
{
"word": "free filter"
},
{
"word": "ultrafilter"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
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],
"glosses": [
"An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
],
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"ultrafilter",
"ultrafilter"
],
[
"cofinite",
"cofinite"
]
],
"qualifier": "especially nonstandard analysis",
"raw_glosses": [
"(mathematical analysis, especially nonstandard analysis) An ultrafilter which contains all cofinite subsets of the set which is being \"filtered\" by it."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
}
],
"word": "free ultrafilter"
}
Download raw JSONL data for free ultrafilter meaning in All languages combined (1.1kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-21 from the enwiktionary dump dated 2025-05-01 using wiktextract (89ebc88 and e74c913). 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.