See clopen on Wiktionary
{ "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": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "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": "quote" }, { "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": "quote" } ], "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" } { "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" ] } ], "head_templates": [ { "args": {}, "expansion": "clopen (plural clopens)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "_dis": "31 69", "kind": "other", "name": "English adjectives ending in -en", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "English blends", "parents": [], "source": "w+disamb" }, { "_dis": "35 65", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "26 74", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "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" ], [ "worker", "worker" ], [ "closing shift", "closing shift" ], [ "opening shift", "opening shift" ] ], "related": [ { "word": "swing shift" } ] } ], "sounds": [ { "ipa": "/ˈkləʊ.pən/", "tags": [ "Received-Pronunciation" ] }, { "ipa": "/ˈkloʊ.pən/", "tags": [ "US" ] }, { "rhymes": "-əʊpən" } ], "wikipedia": [ "Clopen set" ], "word": "clopen" }
{ "categories": [ "English adjectives", "English adjectives ending in -en", "English blends", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English uncomparable adjectives", "Pages with 1 entry", "Pages with entries", "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.", "head_templates": [ { "args": { "1": "-" }, "expansion": "clopen (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ "English terms with quotations", "Quotation templates to be cleaned", "en:Topology" ], "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": "quote" }, { "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": "quote" } ], "glosses": [ "Both open and closed." ], "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" } { "categories": [ "English adjectives", "English adjectives ending in -en", "English blends", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English uncomparable adjectives", "Pages with 1 entry", "Pages with entries", "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" ] } ], "head_templates": [ { "args": {}, "expansion": "clopen (plural clopens)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "swing shift" } ], "senses": [ { "categories": [ "English terms with usage examples" ], "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" }
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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 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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