See uniformly continuous in All languages combined, or Wiktionary
Download JSON data for uniformly continuous meaning in English (4.1kB)
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"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
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{
"text": "A uniformly continuous function is a function whose derivative is bounded.",
"type": "example"
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],
"glosses": [
"That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<δ, it must be the case that D_Y(f(x),f(y))<ϵ (where D_X and D_Y are the metrics of X and Y, respectively)."
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"id": "en-uniformly_continuous-en-adj-CPLCowj7",
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"raw_glosses": [
"(mathematical analysis, of a function from a metric space X to a metric space Y) That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<δ, it must be the case that D_Y(f(x),f(y))<ϵ (where D_X and D_Y are the metrics of X and Y, respectively)."
],
"raw_tags": [
"of a function from a metric space X to a metric space Y"
],
"related": [
{
"word": "uniform continuity"
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"tags": [
"not-comparable"
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"topics": [
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"translations": [
{
"code": "fr",
"lang": "French",
"sense": "property of a function",
"word": "uniformément continu"
},
{
"code": "de",
"lang": "German",
"sense": "property of a function",
"word": "gleichmäßig stetig"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "property of a function",
"word": "egyenletesen folytonos"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "property of a function",
"tags": [
"masculine"
],
"word": "samfelldur í jöfnum mæli"
},
{
"code": "mn",
"lang": "Mongolian",
"roman": "žigd tasraltgüj",
"sense": "property of a function",
"word": "жигд тасралтгүй"
},
{
"code": "pl",
"lang": "Polish",
"sense": "property of a function",
"word": "jednostajnie ciągły"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Cyrillic",
"Ijekavian"
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"word": "ра̏вномјерно не̏прекӣдан"
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{
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},
{
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"sense": "property of a function",
"tags": [
"Cyrillic"
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"word": "једно̀лико не̏прекӣдан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Cyrillic"
],
"word": "у̀нифо̄рмно не̏прекӣдан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
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"Roman"
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"word": "rȁvnomjerno nȅprekīdan"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
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"word": "rȁvnomerno nȅprekīdan"
},
{
"code": "sh",
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"sense": "property of a function",
"tags": [
"Roman"
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"word": "jednòliko nȅprekīdan"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Roman"
],
"word": "ùnifōrmno nȅprekīdan"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "property of a function",
"word": "likformigt kontinuerlig"
}
]
}
],
"word": "uniformly continuous"
}
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],
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"That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<δ, it must be the case that D_Y(f(x),f(y))<ϵ (where D_X and D_Y are the metrics of X and Y, respectively)."
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"(mathematical analysis, of a function from a metric space X to a metric space Y) That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<δ, it must be the case that D_Y(f(x),f(y))<ϵ (where D_X and D_Y are the metrics of X and Y, respectively)."
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"tags": [
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"translations": [
{
"code": "fr",
"lang": "French",
"sense": "property of a function",
"word": "uniformément continu"
},
{
"code": "de",
"lang": "German",
"sense": "property of a function",
"word": "gleichmäßig stetig"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "property of a function",
"word": "egyenletesen folytonos"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "property of a function",
"tags": [
"masculine"
],
"word": "samfelldur í jöfnum mæli"
},
{
"code": "mn",
"lang": "Mongolian",
"roman": "žigd tasraltgüj",
"sense": "property of a function",
"word": "жигд тасралтгүй"
},
{
"code": "pl",
"lang": "Polish",
"sense": "property of a function",
"word": "jednostajnie ciągły"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Cyrillic",
"Ijekavian"
],
"word": "ра̏вномјерно не̏прекӣдан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Cyrillic",
"Ekavian"
],
"word": "ра̏вномерно не̏прекӣдан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Cyrillic"
],
"word": "једно̀лико не̏прекӣдан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Cyrillic"
],
"word": "у̀нифо̄рмно не̏прекӣдан"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Ijekavian",
"Roman"
],
"word": "rȁvnomjerno nȅprekīdan"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Ekavian",
"Roman"
],
"word": "rȁvnomerno nȅprekīdan"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Roman"
],
"word": "jednòliko nȅprekīdan"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "property of a function",
"tags": [
"Roman"
],
"word": "ùnifōrmno nȅprekīdan"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "property of a function",
"word": "likformigt kontinuerlig"
}
],
"word": "uniformly continuous"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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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