Permukaan (topologi)

Sebuah permukaan terbuka dengan x-, y -, dan z- kontur ditampilkan.
Artikel utama: Permukaan (matematika)

Permukaan (bahasa Inggris: surface) dalam matematika, khususnya dalam topologi, adalah suatu kelipatan topologi dalam dua dimensi. Contoh paling umum adalah batas suatu benda padat dalam ruang tiga dimensi biasa R3 — misalnya, permukaan suatu bola. Di sisi lain, ada permukaan-permukaan, seperti botol Klein, yang tidak dapat dimasukkan ke dalam ruang Euklidean tiga dimensi tanpa menyertakan singularitas atau potongan ke diri sendiri.

Definisi

Suatu permukaan (secara topologi) adalah suatu ruang topologi yang setiap titiknya mempunyai satu tangga homeomorfik terbuka terhadap sejumlah subset terbuka pada bidang Euklidean E2. Tetangga semacam itu, bersama dengan homeomorfisme terkait, dikenal sebagai "peta (koordinat)" (coordinate chart). Melalui peta ini maka tetangga itu mendapatkan koordinat standar pada bidang Euklidean. Koordinat-koordinat ini dikenal sebagai koordinat lokal dan homeomorfisme ini membuat permukaan itu dikatakan sebagai secara lokal Euklidean.

Istilah "permukaan" tanpa tambahan kualifikasi merujuk kepada permukaan tanpa batasan. Terutama, suatu permukaan dengan batasan kosong adalah permukaan dalam arti umum. Suatu permukaan dengan batasan kosong yang kompak dikenal sebagai "permukaan tertutup" (closed surface). Bola dua dimensi, torus dua dimensi, danbidang proyeksi real adalah contoh-contoh dari permukaan tertutup.

Lihat pula

Pustaka

Pranala luar

Lihat entri surface di kamus bebas Wiktionary.

Read other articles:

Demain, dès l'aube...

Demain, dès l'aube...karya Victor HugoManuscrik sajakTerbit perdana1847NegaraPrancisBahasaPrancisSeriLes ContemplationsTerbit1856 (1856)Baris12 Demain, dès l'aube..., Besok, begitu fajar menyingsing, adalah salah satu sajak yang paling terkenal oleh penulis asal Prancis Victor Hugo, diterbitkan tahun 1856 dalam karyanya Les Contemplations. Sajak ini terdiri dari tiga ayat empat baris dengan bait yang terdiri dari 12 suku kata yang dalam bahasa Prancis disebut alexandrin. Sajak ini ...

 

Inner Mongolia

Autonomous region of China Autonomous region in ChinaInner MongoliaAutonomous regionInner Mongolia Autonomous RegionName transcription(s) • Chinese内蒙古自治区(Nèi Měnggǔ Zìzhìqū) • Mongolianᠥᠪᠥᠷ ᠮᠣᠩᠭᠣᠯ ᠤᠨᠥᠪᠡᠷᠲᠡᠭᠨ ᠵᠠᠰᠠᠬᠤ ᠣᠷᠣᠨ(Öbür mongγol-un öbertegen jasaqu orun) • AbbreviationNM / 蒙 (Měng)Clockwise from the top left: Steppes in Hulun Buir Greater Khingan range Dazhao Templ...

 

US Sambenedettese

Italian football club Football clubSambenedetteseFull nameAssociazione Sportiva Sambenedettese S.r.l.Nickname(s)SambFounded1923; 101 years ago (1923)1994; 30 years ago (1994) (refounded) 2006; 18 years ago (2006) (refounded)2009; 15 years ago (2009) (refounded)2013; 11 years ago (2013) (refounded)2021; 3 years ago (2021) (refounded)GroundStadio Riviera delle Palme,San Benedetto del Tron...

Mediaset Extra

Mediaset ExtraLogo dell'emittenteStato Italia Linguaitaliano Tipotematico Target15-54 anni[1] SloganIl bello di ieri, il meglio di oggi VersioniMediaset Extra SD 576i (SDTV)(data di lancio: 26 novembre 2010)Mediaset Extra HD 1080i (HDTV)(data di lancio: 1º giugno 2018,14 luglio 2022)Mediaset Extra 2 576i (SDTV)(data di lancio: 11 luglio 2019) Data chiusura1º agosto 2018 (Mediaset Extra HD, 1º lancio)18 gennaio 2020 (Mediaset Extra 2)17 gennaio 2023 (Mediaset Extra SD) GruppoMF...

 

Jan Strelau

Polish psychologist (1931–2020) Jan Strelau Jan Strelau (born 30 May 1931 in Gdańsk; died 4 August 2020 in Warsaw) was a Polish psychologist best known for his studies on temperament. He was professor of psychology at Warsaw University from 1968 to 2001 and was since 2001 professor at Warsaw School of Social Sciences and Humanities, where he took the positions of Vice-rector for Research and International Affairs (2002–2010), Vice-rector for Research (2010–2012), and the Chairman of th...

 

B

  此條目介紹的是拉丁字母中的第2个字母。关于其他用法，请见「B (消歧义)」。   提示：此条目页的主题不是希腊字母Β、西里尔字母В、Б、Ъ、Ь或德语字母ẞ、ß。 BB b(见下)用法書寫系統拉丁字母英文字母ISO基本拉丁字母（英语：ISO basic Latin alphabet）类型全音素文字相关所属語言拉丁语读音方法 [b][p][ɓ](适应变体)Unicode编码U+0042, U+0062字母顺位2数值 2歷史發...

Gerberoy

Gerberoycomune Gerberoy – Veduta LocalizzazioneStato Francia RegioneAlta Francia Dipartimento Oise ArrondissementBeauvais CantoneGrandvilliers TerritorioCoordinate49°32′N 1°51′E / 49.533333°N 1.85°E49.533333; 1.85 (Gerberoy)Coordinate: 49°32′N 1°51′E / 49.533333°N 1.85°E49.533333; 1.85 (Gerberoy) Superficie4,53 km² Abitanti95[1] (2009) Densità20,97 ab./km² Altre informazioniCod. postale60380 Fuso orarioUTC+1 Codic...

 

ECMA International

ECMA InternationalEuropean Computer Manufacturers Association TipoOrganizzazione internazionale Fondazione1961 Sede centrale Ginevra IndirizzoRue du Rhône 114, CH1204 Geneva, Switzerland Sito web Modifica dati su Wikidata · Manuale La ECMA (European Computer Manufacturers Association) è un'associazione fondata nel 1961 e dedicata alla standardizzazione nel settore informatico e dei sistemi di comunicazione. Dal 1994 viene chiamata ECMA International. Indice 1 Attività 2 Membri 3 Note...

 

Metodo di Gauss-Seidel

Questa voce o sezione sull'argomento matematica non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Segui i suggerimenti del progetto di riferimento. In analisi numerica il metodo di Gauss-Seidel è un metodo iterativo, simile al metodo di Jacobi, per la risoluzione di un sistema lineare, scritto nella forma matriciale A x = b . {\displaystyle Ax=b.} Indice ...

Wisden Cricketers' Almanack

British cricket almanac Wisden redirects here. For other uses, see Wisden (disambiguation). Wisden Cricketers' Almanack2019 editionEditorLawrence BoothCategoriesCricketPublisherBloomsburyTotal circulation50,000 (2006)FounderJohn WisdenFirst issue1864; 160 years ago (1864)CountryUnited KingdomBased inLondon, EnglandWebsitewisden.com Wisden Cricketers' Almanack, or simply Wisden, colloquially the Bible of Cricket, is a cricket reference book published annually in the United Ki...

 

Katedral Siedlce

Katedral SiedlceKatedral Santa Perawan Maria Dikandung Tanpa NodaKatedral SiedlceLokasiSiedlceNegaraPolandiaDenominasiGereja Katolik RomaArsitekturStatusKatedralStatus fungsionalAktifAdministrasiKeuskupanKeuskupan Siedlce Katedral Siedlce atau yang bernama resmi Katedral Santa Perawan Maria Dikandung Tanpa Noda adalah sebuah gereja katedral Katolik yang terletak di Siedlce, Polandia. Katedral ini merupakan pusat kedudukan dan takhta bagi Keuskupan Siedlce.[1] Lihat juga Keuskupan Sied...

 

Lake Tawakoni

Lake in Texas, United States Lake TawakoniSunset over Duck CoveLake TawakoniShow map of TexasLake TawakoniShow map of the United StatesLocationHunt / Rains / Van Zandt Counties, TexasCoordinates32°50′45″N 95°56′36″W / 32.84583°N 95.94333°W / 32.84583; -95.94333TypereservoirBasin countriesUnited StatesManaging agencySabine River Authority of TexasFirst floodedOctober 1960 (1960-10)Surface area37,879 acres (15,329 ha)Water volume926,000...

Muhammad al-Baqir

ImamMuhammad al-BaqirFifth imam in Twelver Shi'ism and Isma'ilismمُحَمَّد ٱلْبَاقِرA drawing depicting a delegation of merchants from Khorasan visiting al-Baqir (in the center)5th Shia ImamIn office712–733Preceded byAli al-SajjadSucceeded byJa'far al-Sadiq PersonalBornc. 10 May 676Medina, Hejaz, Umayyad EmpireDiedc. 28 January 732 (aged 57)Medina, Umayyad EmpireCause of deathPoisoning[a]Resting placeJannat al-Baqi, Medina24°28′1″N 39°36′50.21″E...

 

Військово-повітряні сили Ісламської Республіки Іран

Військово-повітряні сили Ісламської Республіки Іран Герб Дата створення / заснування 1979 Офіційна назва перс. نیروی هوایی ارتش جمهوری اسلامی ایران‎ Сфера роботи повітряна війна Країна  Іран Є власником Oghab F.C.d Наступник Islamic Republic of Iran Air Defense Forced На заміну Imperial Iranian Ai...

 

Arctic exploration

Physical exploration of the Arctic region Main article: Exploration The 10 °C (50 °F) mean isotherm in July line (in red) commonly defines the border of the Arctic region. Arctic exploration is the physical exploration of the Arctic region of the Earth. It refers to the historical period during which mankind has explored the region north of the Arctic Circle. Historical records suggest that humankind have explored the northern extremes since 325 BC, when the ancient Greek sailor Pytheas rea...

John MacHale

Catholic bishop (1789 (1791?) – 1881) The Most ReverendJohn MacHaleArchbishop of TuamNative nameIrish: Seán Mac ÉilChurchRoman Catholic ChurchArchdioceseTuamOrdersOrdination1814by Daniel MurrayConsecration1825by Pope Leo XIIPersonal detailsBorn6 March 1789 (or 1791)Tubbernavine, County Mayo, IrelandDied7 November 1881 (aged 90 or 92)Tuam, County Galway, IrelandNationalityIrishDenominationRoman Catholic John MacHale[1] (Irish: Seán Mac Éil;[2] 6 March 1789 (or 1...

 

Arrigny

Arrignycomune Arrigny – Veduta LocalizzazioneStato Francia RegioneGrand Est Dipartimento Marna ArrondissementVitry-le-François CantoneSermaize-les-Bains TerritorioCoordinate48°37′N 4°43′E48°37′N, 4°43′E (Arrigny) Superficie15,78 km² Abitanti274[1] (2009) Densità17,36 ab./km² Altre informazioniCod. postale51290 Fuso orarioUTC+1 Codice INSEE51016 CartografiaArrigny Sito istituzionaleModifica dati su Wikidata · Manuale Arrigny è un comune francese...

 

Andrew Bogut

Australian basketball player (born 1984) Andrew BogutBogut with the Golden State Warriors in 2019Personal informationBorn (1984-11-28) 28 November 1984 (age 39)Melbourne, Victoria, AustraliaListed height7 ft 0 in (2.13 m)Listed weight260 lb (118 kg)Career informationHigh school St John's Regional College(Melbourne, Victoria) Lake Ginninderra(Canberra, Australian Capital Territory) CollegeUtah (2003–2005)NBA draft2005: 1st round, 1st overall pickSelected by the ...

John Bull (composer)

English composer and organist (1562/63–1628) John Bull in c. 1589, portrait kept at the Bate Collection of Musical Instruments John Bull (1562/63 – 12/13 March 1628) was an English composer, organist, virginalist and organ builder.[1] He was a renowned keyboard performer of the virginalist school and most of his compositions were written for this medium. Life and career Bull's place of birth is uncertain. In an article published in 1952, Thurston Dart presumed that Bull's fa...

 

Pokal Nogometne zveze Slovenije 2013-2014

Pokal Slovenije 2013-2014Pokal Nogometne zveze Slovenije 2013./14. Competizione Coppa di Slovenia Sport Calcio Edizione 23ª Organizzatore Federcalcio slovena Date dal 20 agosto 2013al 21 maggio 2014 Luogo  Slovenia Partecipanti 27 Formula Eliminazione diretta Risultati Vincitore Gorica(3º titolo) Secondo Maribor Semi-finalisti Olimpia LubianaRudar Velenje Statistiche Miglior marcatore 4 giocatori a pari merito Incontri disputati 32 Gol segnati 118 (3,69 per incontro)...