See clopen in All languages combined, or Wiktionary
Download JSON data for clopen meaning in English (3.8kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "closed",
"3": "open"
},
"expansion": "Blend of closed + open",
"name": "blend"
}
],
"etymology_text": "Blend of closed + open.",
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "clopen (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Topology",
"orig": "en:Topology",
"parents": [
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}
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"examples": [
{
"ref": "1990, Gerald A Edgar, Measure, Topology, and Fractal Geometry, page 80",
"text": "A subset of a metric space is clopen iff it is both closed and open. A metric space is called zero-dimensional iff there is a base for the open sets consisting of clopen sets.",
"type": "quotation"
},
{
"text": "1999, S. J. Dilworth, On the extensibility of certain homeomorphisms and linear isometries, Krzysztof Jarosz (editor), Function Spaces: Proceedings of the Third Conference on Function Spaces, American Mathematical Society, Contemporary Mathematics, Volume 232, page 124,\nFACT 1. Disjoint closed subsets of ℕN may be separated by disjoint clopen sets."
},
{
"ref": "2002, D. A. Vladimirov, Boolean Algebras in Analysis, page 133",
"text": "Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space #x5C;mathfrak#x7B;Q#x7D; are separated by disjoint clopen sets.\n2) Every algebra of clopen sets which separates the points of a totally disconnected compact space contains all clopen sets.",
"type": "quotation"
}
],
"glosses": [
"Both open and closed."
],
"id": "en-clopen-en-adj-BrT4EKpD",
"links": [
[
"topology",
"topology"
],
[
"set",
"set"
],
[
"topological space",
"topological space"
],
[
"open",
"open"
],
[
"closed",
"closed"
]
],
"raw_glosses": [
"(topology, of a set in a topological space) Both open and closed."
],
"raw_tags": [
"of a set in a topological space"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences",
"topology"
]
}
],
"sounds": [
{
"ipa": "/ˈkləʊ.pən/",
"tags": [
"Received-Pronunciation"
]
},
{
"ipa": "/ˈkloʊ.pən/",
"tags": [
"US"
]
},
{
"rhymes": "-əʊpən"
}
],
"wikipedia": [
"Clopen set"
],
"word": "clopen"
}
{
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},
"expansion": "Blend of closed + open",
"name": "blend"
}
],
"etymology_text": "Blend of closed + open.",
"forms": [
{
"form": "clopens",
"tags": [
"plural"
]
}
],
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{
"args": {},
"expansion": "clopen (plural clopens)",
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],
"lang": "English",
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{
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],
"examples": [
{
"text": "James is on vacation, so I've got to do a clopen this weekend to cover his shifts.",
"type": "example"
}
],
"glosses": [
"A pair of work shifts in which a worker works a closing shift one day and then works an opening shift the following day."
],
"id": "en-clopen-en-noun-GvlYEwVP",
"links": [
[
"work",
"work"
],
[
"shift",
"shift"
],
[
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"worker"
],
[
"closing shift",
"closing shift"
],
[
"opening shift",
"opening shift"
]
],
"related": [
{
"word": "swing shift"
}
]
}
],
"sounds": [
{
"ipa": "/ˈkləʊ.pən/",
"tags": [
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},
{
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},
{
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],
"wikipedia": [
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],
"word": "clopen"
}
{
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{
"ref": "1990, Gerald A Edgar, Measure, Topology, and Fractal Geometry, page 80",
"text": "A subset of a metric space is clopen iff it is both closed and open. A metric space is called zero-dimensional iff there is a base for the open sets consisting of clopen sets.",
"type": "quotation"
},
{
"text": "1999, S. J. Dilworth, On the extensibility of certain homeomorphisms and linear isometries, Krzysztof Jarosz (editor), Function Spaces: Proceedings of the Third Conference on Function Spaces, American Mathematical Society, Contemporary Mathematics, Volume 232, page 124,\nFACT 1. Disjoint closed subsets of ℕN may be separated by disjoint clopen sets."
},
{
"ref": "2002, D. A. Vladimirov, Boolean Algebras in Analysis, page 133",
"text": "Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space #x5C;mathfrak#x7B;Q#x7D; are separated by disjoint clopen sets.\n2) Every algebra of clopen sets which separates the points of a totally disconnected compact space contains all clopen sets.",
"type": "quotation"
}
],
"glosses": [
"Both open and closed."
],
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"topology",
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[
"set",
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"topological space",
"topological space"
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"open",
"open"
],
[
"closed",
"closed"
]
],
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"(topology, of a set in a topological space) Both open and closed."
],
"raw_tags": [
"of a set in a topological space"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences",
"topology"
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}
],
"sounds": [
{
"ipa": "/ˈkləʊ.pən/",
"tags": [
"Received-Pronunciation"
]
},
{
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"tags": [
"US"
]
},
{
"rhymes": "-əʊpən"
}
],
"wikipedia": [
"Clopen set"
],
"word": "clopen"
}
{
"categories": [
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"English entries with language name categories using raw markup",
"English lemmas",
"English nouns",
"English terms with IPA pronunciation",
"English uncomparable adjectives",
"Rhymes:English/əʊpən",
"Rhymes:English/əʊpən/2 syllables"
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "closed",
"3": "open"
},
"expansion": "Blend of closed + open",
"name": "blend"
}
],
"etymology_text": "Blend of closed + open.",
"forms": [
{
"form": "clopens",
"tags": [
"plural"
]
}
],
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{
"args": {},
"expansion": "clopen (plural clopens)",
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"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "swing shift"
}
],
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],
"examples": [
{
"text": "James is on vacation, so I've got to do a clopen this weekend to cover his shifts.",
"type": "example"
}
],
"glosses": [
"A pair of work shifts in which a worker works a closing shift one day and then works an opening shift the following day."
],
"links": [
[
"work",
"work"
],
[
"shift",
"shift"
],
[
"worker",
"worker"
],
[
"closing shift",
"closing shift"
],
[
"opening shift",
"opening shift"
]
]
}
],
"sounds": [
{
"ipa": "/ˈkləʊ.pən/",
"tags": [
"Received-Pronunciation"
]
},
{
"ipa": "/ˈkloʊ.pən/",
"tags": [
"US"
]
},
{
"rhymes": "-əʊpən"
}
],
"wikipedia": [
"Clopen set"
],
"word": "clopen"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 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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