1. Ostrogradski Mikhail Vasilevich Ostrogradski. Born 24 Sept Mikhail Ostrogradskiattended the Poltava Gymnasium secondary school. When the time http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Ostrogradski.html

Mikhail Vasilevich Ostrogradski Born: 24 Sept 1801 in Pashennaya (now Poltava oblast), Ukraine Died: 1 Jan 1862 in Poltava (now Ukraine) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Mikhail Ostrogradski attended the Poltava Gymnasium secondary school. When the time came for him to leave, he expressed a wish to have a military career. However his family was not wealthy and it was felt that a soldier's pay was not good enough. Eventually it was decided that he should take up a career in the civil service and in order to obtain a high ranking position a university education was necessary. Ostrogradski entered the University of Kharkov in 1816 and studied physics and mathematics. In 1820 he took and passed the exams necessary for his degree but the minister of religious affairs and national education refused to confirm the decision and required him to retake the examinations. The problem appears to have been his mathematics teacher Osipovsky who, in the year 1820, was suspended from his post on religious grounds. The officials who made this decision made

2. Introdução Ostrogradski Mikhail Vasilevich Ostrogradski Nasceu 24 Setembro de 1801 em Pashennaya (agora Poltava oblast), Ukraine Faleceu 1 Janeiro de 1862 in Poltava (agora Ukraine) http://cabril.fam.ulusiada.pt/Dep/eei/cadeiras/teoriaelect/9900/trab08/introOst.

Página Inicial Biografia Bibliografia Local de Nascimento ... Links Mikhail Vasilevich Ostrogradski Nasceu: 24 Setembro de 1801 em Pashennaya (agora Poltava oblast), Ukraine Faleceu: 1 Janeiro de 1862 in Poltava (agora Ukraine) Página Inicial Biografia Bibliografia Local de Nascimento ... Links

3. References For Ostrogradski References for mikhail ostrogradski. Biography in Dictionary of ScientificBiography (New York 19701990). Books AP Youschkevitch http://www.mathsoc.spb.ru/pantheon/ostrogra/ref.html

References for Mikhail Ostrogradski Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: A P Youschkevitch, Michel Ostrogradski et le progres de la science au XIXe siecle (Paris, 1966). Articles: V I Antropova, Remarks on M V Ostrogradskii's 'Memoir on heat diffusion in solid bodies' (Russian), Istor.-Mat. Issled. Y L Geronimus, Mikhail Vasilevich Ostrogradski, Essays on the Works of the Leading Figures in Russian Mechanics (Moscow, 1952), 13-57. B V Gnedenko, On M V Ostrogradskii 's works on the theory of probability (Russian), Istor.-Mat. Issled. B V Gnedenko, Mihail Vasil' evic Ostrogradskii (Russian), Uspehi Matem. Nauk (N.S.) A T Grigorian, The works of M V Ostrogradskii in the realm of mathematics (Polish), Kwart. Hist. Nauki i Tech. S N Kiro, An equation of M V Ostrogradskii in the mathematical theory of heat conduction (Russian), Voprosy Istor. Estestvoznan. i Tehn. I Z Stokalo, Works of M V Ostrogradskii in mathematical physics (Russian), Ukrain Mat. Zurnal

4. Lebensdaten Von Mathematikern Osgood, William Menabrea, Luigi Muir, Thomas ostrogradski, mikhail Menaechmus Mydorge, Claude Oughtred, William Menelaus http://www.mathe.tu-freiberg.de/~hebisch/cafe/lebensdaten.html

Diese Seite ist dem Andenken meines Vaters Otto Hebisch (1917 - 1998) gewidmet. By our fathers and their fathers in some old and distant town from places no one here remembers come the things we've handed down. Marc Cohn Dies ist eine Sammlung, die aus verschiedenen Quellen stammt, u. a. aus Jean Dieudonne, Geschichte der Mathematik, 1700 - 1900, VEB Deutscher Verlag der Wissenschaften, Berlin 1985. Helmut Gericke, Mathematik in Antike und Orient - Mathematik im Abendland, Fourier Verlag, Wiesbaden 1992. Otto Toeplitz, Die Entwicklung der Infinitesimalrechnung, Springer, Berlin 1949. MacTutor History of Mathematics archive A B C ... Z Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843)

5. Ostrogradski Portraits mikhail ostrogradski. This is taken from a Russian stamp. JOC/EFRAugust 2001 The URL of this page is © Copyright information. http http://www-gap.dcs.st-and.ac.uk/~history/PictDisplay/Ostrogradski.html

Mikhail Ostrogradski This is taken from a Russian stamp JOC/EFR August 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Ostrogradski.html

6. Ostrogradski Biography of mikhail ostrogradski (18011862) Main index. mikhail ostrogradski attended the Poltava Gymnasium secondary school. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ostrogradski.html

Mikhail Vasilevich Ostrogradski Born: 24 Sept 1801 in Pashennaya (now Poltava oblast), Ukraine Died: 1 Jan 1862 in Poltava (now Ukraine) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Mikhail Ostrogradski attended the Poltava Gymnasium secondary school. When the time came for him to leave, he expressed a wish to have a military career. However his family was not wealthy and it was felt that a soldier's pay was not good enough. Eventually it was decided that he should take up a career in the civil service and in order to obtain a high ranking position a university education was necessary. Ostrogradski entered the University of Kharkov in 1816 and studied physics and mathematics. In 1820 he took and passed the exams necessary for his degree but the minister of religious affairs and national education refused to confirm the decision and required him to retake the examinations. The problem appears to have been his mathematics teacher Osipovsky who, in the year 1820, was suspended from his post on religious grounds. The officials who made this decision made

7. Biography-center - Letter O doctor.cfm/2291.html; ostrogradski, mikhail wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/ostrogradski.html;Ostwald, Wilhelm www http://www.biography-center.com/o.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish O 134 biographies O'Brian, Patrick www.wwnorton.com/pob/bio.htm O'Brien, Margaret www.wic.org/bio/mobrien.htm O'connor, Justice supct.law.cornell.edu/supct/justices/oconnor.bio.clr.html O'Connor, Flannery www.wwnorton.com/naal/explore/oconnor.htm O'Connor, Mary Flannery cheshire.cwrl.utexas.edu/~mmaynard/voices/oconnor.html O'Hara, John www.ncteamericancollection.org/litmap/ohara_john_pa.htm O'Hara, Catherine www.northernstars.ca/actorsmno/oharabio.html O'Keeffe, Georgia www.pbs.org/wnet/americanmasters/database/okeeffe_g.html O'Keeffe, Georgia www.geocities.com/moondarlin/artokeeffe.html O'Neill, Terri library.thinkquest.org/20117/oneill.html O'Neill, Eugene odur.let.rug.nl/~usa/LIT/oneill.htm_pa.htm O'Neill, Eugene

8. References For Ostrogradski References for the biography of mikhail ostrogradski References for mikhail ostrogradski. Biography in Dictionary of Scientific Biography (New York 19701990). http://www-history.mcs.st-and.ac.uk/~history/References/Ostrogradski.html

References for Mikhail Ostrogradski Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: A P Youschkevitch, Michel Ostrogradski et le progres de la science au XIXe siecle (Paris, 1966). Articles: V I Antropova, Remarks on M V Ostrogradskii's 'Memoir on heat diffusion in solid bodies' (Russian), Istor.-Mat. Issled. Y L Geronimus, Mikhail Vasilevich Ostrogradski, Essays on the Works of the Leading Figures in Russian Mechanics (Moscow, 1952), 13-57. B V Gnedenko, On M V Ostrogradskii 's works on the theory of probability (Russian), Istor.-Mat. Issled. B V Gnedenko, Mihail Vasil' evic Ostrogradskii (Russian), Uspehi Matem. Nauk (N.S.) A T Grigorian, The works of M V Ostrogradskii in the realm of mathematics (Polish), Kwart. Hist. Nauki i Tech. S N Kiro, An equation of M V Ostrogradskii in the mathematical theory of heat conduction (Russian), Voprosy Istor. Estestvoznan. i Tehn. I Z Stokalo, Works of M V Ostrogradskii in mathematical physics (Russian), Ukrain Mat. Zurnal Main index Birthplace Maps Biographies Index History Topics ... Societies, honours, etc.

9. Teorema Ostrogradski Translate this page Teorema de ostrogradski. ostrogradski ,mikhail (1801-1861). MatemáticoRusso que descobriu o teorema de Green independentemente de http://www.fam.ulusiada.pt/Dep/eei/cadeiras/teoriaelect/9900/trab08/teoOst.htm

Página Inicial Introdução Ostrogradski Função de Ostrogradsk i]] Teorema de Ostrogradski Ostrogradski ,Mikhail (1801-1861) Matemático Russo que descobriu o teorema de Green independentemente de Green,sendo na Russia depois conhecido como teorema de Ostragradski. Teorema de Ostragradski Teorema de Ostragradski é um vector identidade equivalente ao teorema de Curl no plano numa região D com limite: Se a região D está na esquerda quando circula á volta Então a área pode ser usada do seguinte modo: Página Inicial Introdução Ostrogradski Função de Ostrogradsk i]]

10. Ostrogradski Portraits Portraits of mikhail ostrogradski mikhail ostrogradski. This is taken from a Russian stamp http://www-history.mcs.st-and.ac.uk/history/PictDisplay/Ostrogradski.html

Mikhail Ostrogradski This is taken from a Russian stamp JOC/EFR August 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Ostrogradski.html

11. Introdução Ostrogradski Translate this page mikhail Vasilevich ostrogradski. Nasceu 24 Setembro de 1801 em Pashennaya (agoraPoltava oblast), Ukraine. Faleceu 1 Janeiro de 1862 in Poltava (agora Ukraine). http://www.fam.ulusiada.pt/Dep/eei/cadeiras/teoriaelect/9900/trab08/introOst.htm

Página Inicial Biografia Bibliografia Local de Nascimento ... Links Mikhail Vasilevich Ostrogradski Nasceu: 24 Setembro de 1801 em Pashennaya (agora Poltava oblast), Ukraine Faleceu: 1 Janeiro de 1862 in Poltava (agora Ukraine) Página Inicial Biografia Bibliografia Local de Nascimento ... Links

12. OPE-MAT - Historique Translate this page Ernst Moufang, Ruth Ortega, Juan de Mellin, Hjalmar Mouton, Gabriel Osgood, WilliamMenabrea, Luigi Muir, Thomas ostrogradski, mikhail Menaechmus Mydorge http://www.gci.ulaval.ca/PIIP/math-app/Historique/mat.htm

A Abel , Niels Akhiezer , Naum Anthemius of Tralles Abraham bar Hiyya al'Battani , Abu Allah Antiphon the Sophist Abraham, Max al'Biruni , Abu Arrayhan Apollonius of Perga Abu Kamil Shuja al'Haitam , Abu Ali Appell , Paul Abu'l-Wafa al'Buzjani al'Kashi , Ghiyath Arago , Francois Ackermann , Wilhelm al'Khwarizmi , Abu Arbogast , Louis Adams , John Couch Albert of Saxony Arbuthnot , John Adelard of Bath Albert , Abraham Archimedes of Syracuse Adler , August Alberti , Leone Battista Archytas of Tarentum Adrain , Robert Albertus Magnus, Saint Argand , Jean Aepinus , Franz Alcuin of York Aristaeus the Elder Agnesi , Maria Alekandrov , Pavel Aristarchus of Samos Ahmed ibn Yusuf Alexander , James Aristotle Ahmes Arnauld , Antoine Aida Yasuaki Amsler , Jacob Aronhold , Siegfried Aiken , Howard Anaxagoras of Clazomenae Artin , Emil Airy , George Anderson , Oskar Aryabhata the Elder Aitken , Alexander Angeli , Stefano degli Atwood , George Ajima , Chokuyen Anstice , Robert Richard Avicenna , Abu Ali B Babbage , Charles Betti , Enrico Bossut , Charles Bachet Beurling , Arne Bouguer , Pierre Bachmann , Paul Boulliau , Ismael Bacon , Roger Bhaskara Bouquet , Jean Backus , John Bianchi , Luigi Bour , Edmond Baer , Reinhold Bieberbach , Ludwig Bourgainville , Louis Baire Billy , Jacques de Boutroux , Pierre Baker , Henry Binet , Jacques Bowditch , Nathaniel Ball , W W Rouse Biot , Jean-Baptiste Bowen , Rufus Balmer , Johann Birkhoff , George Boyle , Robert Banach , Stefan Bjerknes, Carl

13. Mathem_abbrev Noether, Emmy. Ockham, William of Oka, Kiyoshi, Omar Khayyam Ortega,Juan de, ostrogradski, mikhail Oughtred, William. Pacioli, Luca http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm

Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive. Some suggestions on the historical perspective might be: (a) Any wars etc. (b) Scientific breakthroughs of the time (c) Major discoveries of the time (d) How did this mathematician change history etc.

14. Mostra Eventos Da Data Selecionada Translate this page 24/09/1896 - Nascimento de Tadeusz Wazewski (matemático polonês) 24/09/1901 -Nascimento de mikhail Vasilevich ostrogradski (matemático ucraniano) 25/09 http://www.ponteiro.com.br/mostrad8.php?w=13&pg=8

15. Mostra Eventos Da Data Selecionada Translate this page de Tadeusz Wazewski (matemático polonês) 24/09/1901 Nascimento Matemática - Nascimentode mikhail Vasilevich ostrogradski (matemático ucraniano) 24/09/1903 http://www.ponteiro.com.br/sig07.php

Pesquisando signo de Libra - Encontradas 760 ocorrências. Mostrando de 1 até 50 Setembro    September  Septiembre  Septembre  Settembre  September Nascimento de William Wallace (matemático escocês) Nascimento de Mariano Moreno (jurista argentino) Nascimento de Bento Gonçalves (militar gaúcho - líder da revolta dos farrapos) Nascimento de Armand Hyppolyte Louis Fizeau (físico francês) Nascimento de Mikhail Mikhailovich Ivanov (compositor russo) Nascimento de Richard Karl Wilhelm Theodor von Hertwig (biólogo alemão) Nascimento de Suzanne Valadon (pintora francesa) Nascimento de Walter Lippmann (jornalista norte-americano) Nascimento de Friedrich Paulus (marechal alemão) Nascimento do Papa Paulo VI (Giovanni Batista Monttini) Nascimento de David van Dantzig (matemático holandês) Nascimento de Jaroslav Seifert (poeta tcheco - prêmio Nobel em 1984) Nascimento de Jeno Nenessey (compositor húngaro) Nascimento de Alexey Davidovich Machavariani (compositor georgiano) Nascimento de Omar Ali Saifuddin Sa´adul Khairi Waddien (sultão de Brunei 1950-1967) Nascimento de Aldo Moro (5 vezes primeiro-ministro da Itália) Nascimento de John Coltrane (saxofonista norte-americano) Nascimento de Pierre Marietan (compositor suíço) Nascimento de Romy Schneider (atriz vienense) Nascimento de Bruce Springsteen (cantor popular norte-americano) Nascimento de Hortência de Fátima Marcari (jogadora de basquete) Nascimento de William C. McCool (astronauta norte-americano)

16. Full Alphabetical Index Translate this page Timofei (187). ostrogradski, mikhail (528*) Oughtred, William (654*)Ovidio, Enrico D' (414) Ozanam, Jacques (263). PQ. Pacioli, Luca http://www.geocities.com/Heartland/Plains/4142/matematici.html

Completo Indice Alfabetico Cliccare su una lettera sottostante per andare a quel file. A B C D ... XYZ Cliccare sotto per andare agli indici alfabetici separati A B C D ... XYZ Il numero di parole nella biografia e' dato in parentesi. Un * indica che c'e' un ritratto. A Abbe , Ernst (602*) Abel , Niels Henrik (286*) Abraham bar Hiyya (240) Abraham, Max Abu Kamil Shuja (59) Abu'l-Wafa al'Buzjani (243) Ackermann , Wilhelm (196) Adams, John Couch Adams, Frank Adelard of Bath (89) Adler , August (114) Adrain , Robert (79) Aepinus , Franz (124) Agnesi , Maria (196*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (60) Ahmes Aida Yasuaki (114) Aiken , Howard (94) Airy , George (313*) Aitken , Alexander (825*) Ajima , Chokuyen (144) Akhiezer , Naum Il'ich (248*) al'Battani , Abu Allah (194) al'Biruni , Abu Arrayhan (306*) al'Haitam , Abu Ali (269*) al'Kashi , Ghiyath (73) al'Khwarizmi , Abu (123*) Albanese , Giacomo (282) Albert of Saxony Albert, Abraham Adrian (121*) (158*) Alberti , Leone (181*) Alberto Magno, San (109*) Alcuin di York (237*) Aleksandrov , Pave (160*) Alembert , Jean d' (291*) Alexander , James (163) Amringe , Howard van (354*) Amsler , Jacob (82) Anassagora di Clazomenae (169) Anderson , Oskar (67) Andreev , Konstantin (117) Angeli , Stefano degli (234) Anstice , Robert (209) Antemio of Tralles (55) Antifone il Sofista (125) Apollonio di Perga (276) Appell , Paul (1377) Arago , Dominique (345*) Arbogasto , Louis (87) Arbuthnot , John (251*) Archimede di Siracusa (467*) Archita of Tarentum (103) Argand , Jean (81) Aristeo il Vecchio (44) Aristarco di Samo (183) Aristotele Arnauld , Antoine (179)

17. A Fate Of The Great Mathematical Discoveries rector Mr. Lobatchevski was published. Nikolay Lobatchevski (1792 1856), mikhail ostrogradski (1801 - 1862). And during all his life http://www.goldenmuseum.com/1103MathDiscover_engl.html

A fate of the great mathematical discoveries Nikolay Lobatchevski (1792 - 1856) Mikhail Ostrogradski (1801 - 1862) And during all his life Lobatchevski was subjected to ridicule on the part of the official Russian academic science of that period. Lobatchevski's recognition came from the West science due the genius mathematician Gauss who became the only mathematician who could access properly Lobatchevski's works in geometry. According to Gauss' proposal Lobatchevski was chosen by the Corresponding Member of the Gettingen scientific society. It was other example from the history of the French 19th century mathematics. The name of the French mathematician Evarist Galois is well-known in mathematics. His mathematical works gave the origin of modern algebra. However at his life Evarist Galois was well-known as revolutionary. For public speeches against royal regime he was twice in prison. In 1832 in the age of 21 he was killed on the duel organized by his enemies. His basic mathematical works named later by his name Evarist Galois obtained in the age of 16-18 when he studied in the Lyceum. Galois sent his works to the Paris Academy of Sciences. However even the greatest French mathematicians Cauchy and Fourier cannot understand Galois works. According to legend, academician Cauchy threw out all mathematical Galois' works to the garbage. Cauchy (1789 - 1857) Galois (1811-1832) Galois' works were read and published for 14 years later of his died. In 1870, that is for 38 years later of his died the famous French mathematician Jordan wrote the book on mathematical Galois' investigations and due this book Galois' theory became common property of the world.

18. TLW's 1860s (1860-1869) Timeline 23. German mathematician Eduard Study (d. 1930) on Mar. 23. Politicians.Deaths Russian mathematician mikhail ostrogradski on Jan. http://www.tlwinslow.com/timeline/time186x.html

T.L. Winslow's World History Timeline 1860-1869 C.E. TLW's Great Track of Time Homepage Return to Beginning The U.S. Federal Census of 1860 gives the white population as 31,443,790, and the black population as 4,441,790; free blacks 488,000; the over-65 population is 2.7 percent of the total (849,000); there are 1.3 million German immigrants in the U.S.; American cotton production is 4.5 million bales, up from 3000 in 1790. The population of New York City is 805,000. Mechanization of agriculture causes a billion acres of land to come under cultivation worldwide by 1920, and another billion by 1980 - too bad it's too late for the American South to divest itself of slavery gracefully. The Second Maori War with the British in New Zealand begins in Feb. (ends 1861). The Pony Express begins service between Sacramento and Saint Joseph on Apr. 3 (ends Oct. 24, 1861). Smallpox epidemic in Pennsylvania (ends 1861). On Feb. 27 beardless Abraham Lincoln gives a speech at the Cooper Union in New York City, followed by a speech on Mar. 6 in New Haven , Connecticut, establishing him as a viable candidate for the Republican presidential nomination . The Democratic Party Convention opens in Charleston on Apr. 23, then splits on May 23 into northern and southern sections; the northern section holds its convention in Baltimore on June 18, nominating Illinois Senator

19. UKRINFORM News From Ukraine NATIONAL UNIVERSITY HOSTS INTERNATIONAL CONFERENCE OF MATHEMATICIANS, DEDICATEDTO 200TH ANNIVERSARY OF BIRTH OF mikhail ostrogradski, OUTSTANDING UKRAINIAN http://www.ukremb.com/news/Ukrinform/2001/august/290801UI2.htm

20. SIF5005 Matematikk 2 For F1 2001 Divergensteoremet omtales også gjerne som Johann Carl Friedrich Gauss' teorem,mens andre gjerne gir æren til mikhail Vasilevich ostrogradski. http://www.math.ntnu.no/~hanche/kurs/mat2/2001v/forelesninger.html

Forelesninger - notater i for- og etterkant Synes du forelesningene er en ørkenvandring? Men det er da vakkert i ørkenen! (Men det er farlig og - mye å stikke seg på.) Første til fjerde uke (uke 4-6) Femte til åttende uke (uke 7-10) Åttende til tolvte uke (uke 11-14) Uke 15 var påskeferie til og med tirsdag i uke 16. Trettende «uke» (uke 16/17) Avsnitt 15.7 fortsatt: Rotasjonsfri og konservative vektorfelt i tre dimensjoner gjenstår. Avsnitt 15.6: Divergensteoremet - et fundamentalteorem for trippelintegralet. (torsdag) Avsnitt 15.7 om rotasjonsfri og konservative vektorfelt i tre dimensjoner. For et kontinuerlig deriverbart vektorfelt F definert på et enkeltsammenhengende område er følgende tre krav ekvivalente: Integralet av F mellom to punkter er uavhengig av veien, F er gradienten til en skalar funksjon, curl F F er rotasjonsfri Faktisk er de to første kravene ekvivalente uten av vi legger noe krav på området, og de impliserer det tredje kravet (om F er en gradient så er det tredje kravet bare likhet av annen ordens blandede partiellderiverte for potentialet). Men for at vi skal kunne konkludere tilbake fra det tredje kravet til de to første må vi kreve at definisjonsområdet til F er enkeltsammenhengende : Det vil si at for to veier med samme start- og endepunkt kan alltid den ene deformeres kontinuerlig over i den andre med endepunktene fastholdt, og uten å gå utenfor definisjonsområdet.

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