Katětov–Tong insertion theorem

The Katětov–Tong insertion theorem[1][2][3] is a theorem of point-set topology proved independently by Miroslav Katětov and Hing Tong in the 1950s. The theorem states the following:

Let be a normal topological space and let be functions with upper semicontinuous, lower semicontinuous, and . Then there exists a continuous function with

This theorem has a number of applications and is the first of many classical insertion theorems. In particular it implies the Tietze extension theorem and consequently Urysohn's lemma, and so the conclusion of the theorem is equivalent to normality.

References

  1. ^ Miroslav Katětov, On real-valued functions in topological spaces, Fundamenta Mathematicae 38(1951), 85–91. [1]; Correction to "On real-valued functions in topological spaces", Fundamenta Mathematicae 40(1953), 203–205. [2]
  2. ^ Hing Tong, Some characterizations of normal and perfectly normal spaces, Duke Mathematical Journal 19(1952), 289–292. doi:10.1215/S0012-7094-52-01928-5
  3. ^ Good, Chris; Stares, Ian. "New proofs of classical insertion theorems".

Read other articles:

A Descriptive Vocabulary of the Language in Common Use Amongst the Aborigines of Western Australia

A Descriptive Vocabulary of the Language in Common Use Amongst the Aborigines of Western Australia AuthorGeorge Fletcher MooreCountryEnglandLanguageEnglishPublisherWilliam S. Orr & Co.Publication date1842Media typePrintTextA Descriptive Vocabulary of the Language in Common Use Amongst the Aborigines of Western Australia at Wikisource A Descriptive Vocabulary of the Language in Common Use Amongst the Aborigines of Western Australia is a book by George Fletcher Moore. First published i...

 

Bandar Udara Jalaluddin

Bandar Udara JalaluddinJalaluddin AirportIATA: GTOICAO: WAMGWMO: 97048InformasiJenisPublikPemilikKementerian PerhubunganPengelolaDirektorat Jenderal Perhubungan UdaraMelayaniKabupaten GorontaloLokasiGorontalo, IndonesiaKetinggian dpl18 mdplKoordinat00°38′14″N 122°50′59.5″E / 0.63722°N 122.849861°E / 0.63722; 122.849861Situs webdjalaluddin.comPetaSulawesi daerah di IndonesiaGTOLokasi bandara di Gorontalo / IndonesiaTampilkan peta SulawesiGTOGTO (In...

 

Durham City RFC

English rugby union club Rugby teamDurham CityFull nameDurham City Rugby Football ClubUnionDurham County Rugby Football UnionFounded1872; 152 years ago (1872)LocationDurham, County Durham, EnglandGround(s)Hollow Drift (Capacity: 1,500 (500 seats))League(s)North 1 East2019–2011th Team kit Official websitewww.pitchero.com/clubs/durhamcityrugbyfootballclub Durham City Rugby Football Club is a rugby union club based in the city of Durham, County Durham. The first XV currently ...

Koninklijke TESO

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2022. Texels Eigen Stoomboot OndernemingIndustriTransportasiPendahuluNieuwe Texelsche StoombootdienstDidirikan1907KantorpusatDen Hoorn, BelandaWilayah operasiLaut UtaraJasaAngkutan orangAngkutan barangSitus webwww.teso.nl Dokter Wagemaker milik TESO Koninkli...

 

Sonjay Dutt

Pour les articles homonymes, voir Dutt. Sonjay DuttDonnées généralesNom de naissance Retech BhallaNom de ring Sonjay DuttMonster JNationalité AméricainNaissance 7 avril 1982 (42 ans)WashingtonTaille 5′ 8″ (1,73 m)[1],[2],[3]Poids entre 185 lb (84 kg)[3] et 194 lb (88 kg)[1],[2]Catcheur en activitéFédération All Elite WrestlingTotal Nonstop Action WrestlingEntraîneur KYDA Wrestling School[2]Larry Sharpe[2]Carrière pro. 2000 - aujourd'huimodifie...

 

Athlītikī Enōsis Kōnstantinoupoleōs 2019-2020

Voce principale: Athlītikī Enōsis Kōnstantinoupoleōs. AEK AteneStagione 2019-2020 Sport calcio SquadraPodosfairiki Anonymi Etaireia Athlitiki Enosis Konstantinoupoleos Allenatore Miguel Cardoso(1º luglio - 25 agosto 2019) poi Nikos Kōstenoglou(26 agosto - 6 dicembre 2019) poi Massimo Carrera Presidente Evangelos Aslanidis Souper Ligka Ellada3º posto Coppa di GreciaFinale Europa LeagueFase a gironi Maggiori presenzeCampionato: Mpakakīs (22)Totale: Livaja (28) Miglior marcatoreCampion...

Momoland

Artikel ini perlu dikembangkan dari artikel terkait di Wikipedia bahasa Inggris. (10 Desember 2022) klik [tampil] untuk melihat petunjuk sebelum menerjemahkan. Lihat versi terjemahan mesin dari artikel bahasa Inggris. Terjemahan mesin Google adalah titik awal yang berguna untuk terjemahan, tapi penerjemah harus merevisi kesalahan yang diperlukan dan meyakinkan bahwa hasil terjemahan tersebut akurat, bukan hanya salin-tempel teks hasil terjemahan mesin ke dalam Wikipedia bahasa Indonesia....

 

Corney Grain

British entertainer Richard Corney GrainRichard Corney Grain, 1880sBorn(1844-10-26)26 October 1844TevershamDied16 March 1895(1895-03-16) (aged 50)LondonOccupation(s)entertainer, songwriter Richard Corney Grain (26 October 1844 – 16 March 1895), known by his stage name Corney Grain, was an entertainer and songwriter of the late Victorian era. Biography Corney Grain (left) and Alfred German Reed (right) portrayed in Entr'acte in 1895, the year they both died Born at Teversham in Cambridg...

 

Athis-Mons

Commune in Île-de-France, France Commune in Île-de-France, FranceAthis-MonsCommuneAn aerial view of Athis-Mons Coat of armsLocation (in red) within Paris inner and outer suburbsLocation of Athis-Mons Athis-MonsShow map of FranceAthis-MonsShow map of Île-de-France (region)Coordinates: 48°42′27″N 2°23′20″E / 48.7074°N 2.3889°E / 48.7074; 2.3889CountryFranceRegionÎle-de-FranceDepartmentEssonneArrondissementPalaiseauCantonAthis-MonsIntercommunalityGrand Par...

Giovanni e Paolo

Disambiguazione – Santi Giovanni e Paolo rimanda qui. Se stai cercando altri significati, vedi Santi Giovanni e Paolo (disambigua). Santi Giovanni e PaoloIl martirio dei santi Giovanni e Paolo, Guercino (1632) Martiri  MorteRoma, 26 giugno 362 Venerato daChiesa cattolica Santuario principaleBasilica dei Santi Giovanni e Paolo al Celio Ricorrenza26 giugno Manuale San Zanipolo, Venezia Giovanni e Paolo (morti a Roma il 26 giugno 362) sono due martiri cristiani del IV secolo...

 

コルク

この記事は検証可能な参考文献や出典が全く示されていないか、不十分です。出典を追加して記事の信頼性向上にご協力ください。（このテンプレートの使い方）出典検索?: コルク – ニュース · 書籍 · スカラー · CiNii · J-STAGE · NDL · dlib.jp · ジャパンサーチ · TWL（2017年4月） コルクを打ち抜いて作った瓶の栓 コルク（木栓、�...

 

List of forms of alternative medicine

This article is part of a series onAlternative medicine General information Alternative medicine History Terminology Alternative veterinary medicine Quackery (health fraud) Rise of modern medicine Pseudoscience Antiscience Skepticism Scientific Therapeutic nihilism Fringe medicine and science Acupressure Acupuncture Alkaline diet Anthroposophic medicine Apitherapy Applied kinesiology Aromatherapy Association for Research and Enlightenment Auriculotherapy Bates method Biological terrain asses...

俄亥俄州

  「俄亥俄」重定向至此。关于其他用法，请见「俄亥俄 (消歧义)」。 俄亥俄州 美國联邦州State of Ohio 州旗州徽綽號：七葉果之州地图中高亮部分为俄亥俄州坐标：38°27'N－41°58'N, 80°32'W－84°49'W国家 美國加入聯邦1803年3月1日，在1953年8月7日追溯頒定（第17个加入联邦）首府哥倫布（及最大城市）政府 • 州长（英语：List of Governors of {{{Name}}}]]） •&...

 

Team Sapura Cycling

Malaysian cycling team Team Sapura CyclingTeam informationUCI codeTSCRegisteredMalaysiaFounded2017Discipline(s)RoadStatusUCI ContinentalBicyclesCervéloComponentsShimanoKey personnelGeneral managerSayuti ZahitTeam manager(s)Fairoz Abd GhaniMohd Mahazir HamadMohd Azlan JamalludinTeam name history2017–Team Sapura Cycling Team Sapura Cycling is a Malaysian UCI Continental cycling team founded in 2017 with major backing from Sapura Holdings Berhad, a renowned conglomerate from Malaysia.[1&#...

 

76e parallèle nord

Pour les articles homonymes, voir 76e parallèle. 180° 135°W 90°W 45°W 0° 45°E 90°E 135°E 180°Tracé du parallèle de 76° nord En géographie, le 76e parallèle nord est le parallèle joignant les points de la surface de la Terre dont la latitude est égale à 76° nord. Géographie Dimensions Dans le système géodésique WGS 84, au niveau de 76° de latitude nord, un degré de longitude équivaut à 27,016 km[1] ; la longueur totale du parallèle est donc de 9 ...

Chiclayo

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Chiclayo – news · newspapers · books · scholar · JSTOR (September 2018) (Learn how and when to remove this message) Place in Lambayeque, PeruChiclayo Santa María de los Valles de ChiclayoClockwise from top left: Chiclayo Cathedral, also known as Santa María C...

 

Jan Hus

Pour les articles homonymes, voir Hus. Jan HusJan Hus au bûcher, enluminure du XVe siècle.FonctionProfesseurBiographieNaissance Vers 1371Husinec (royaume de Bohême, Saint-Empire romain germanique)Décès 6 juillet 1415Constance (Principauté épiscopale de Constance, Saint-Empire romain germanique)Sépulture RhinPseudonyme Paulus ConstantiusDomicile Birth house of Jan Hus (d)Formation Université Charles de Prague (baccalauréat universitaire) (jusqu'en 1393)Activités Traducteur, li...

 

Jussi Halla-aho

Finnish politician (b. 1971) Jussi Halla-ahoHalla-aho in 2023Speaker of the Parliament of FinlandIncumbentAssumed office 21 June 2023Preceded byPetteri OrpoLeader of the Finns PartyIn office10 June 2017 – 14 August 2021Preceded byTimo SoiniSucceeded byRiikka PurraMember of Parliamentfor HelsinkiIncumbentAssumed office 3 July 2019In office19 April 2011 – 30 June 2014Succeeded byMika RaatikainenMember of the European Parliamentfor FinlandIn office1 July 2014 �...

John Egerton, 3rd Earl of Bridgewater

English politician (1646–1701) The Right HonourableThe Earl of BridgewaterKB PCFirst Lord of the AdmiraltyIn office1699–1701Preceded byThe Earl of OrfordSucceeded byThe Earl of PembrokeFirst Lord of TradeIn office16 December 1695 – 9 June 1699Preceded byVacant Last held byThe Earl of ShaftesburySucceeded byThe Earl of StamfordMember of Parliament for Buckinghamshire With Thomas WartonIn office1685–1686Preceded byRichard HampdenSucceeded byThomas Lee Personal detailsBorn9 Nove...

 

GR-113808

Chemical compound GR-113808Identifiers IUPAC name 1-(2-methylsulfonylaminoethyl-4-piperidinyl)methyl-1-methyl-1H-indole-3-carboxylate CAS Number144625-51-4PubChem CID119376IUPHAR/BPS247ChemSpider106623UNIIZT350OYT3ICompTox Dashboard (EPA)DTXSID40162772 Chemical and physical dataFormulaC19H27N3O4SMolar mass393.50 g·mol−13D model (JSmol)Interactive image SMILES c13ccccc3c(cn1C)C(=O)OCC(CC2)CCN2CCNS(=O)(C)=O InChI InChI=1S/C19H27N3O4S/c1-21-13-17(16-5-3-4-6-18(16)21)19(23)26-14-15-7-10-2...