Topology: A Very Short Introduction - Web Education
Topology: A Very Short Introduction
VERY SHORT INTRODUCTIONS are for anyone wanting a stimulating and accessible way into a newsubject. They are written by experts, and have been translated into more than 45 different languages.The series began in 1995, and now covers a wide variety of topics in every discipline. The VSIlibrary currently contains over 600 volumes—a Very Short Introduction to everything from Psychologyand Philosophy of Science to American History and Relativity—and continues to grow in every subjectarea.Very Short Introductions available now:ABOLITIONISM Richard S. NewmanTHE ABRAHAMIC RELIGIONS Charles L. CohenACCOUNTING Christopher NobesADAM SMITH Christopher J. BerryADOLESCENCE Peter K. SmithADVERTISING Winston FletcherAESTHETICS Bence NanayAFRICAN AMERICAN RELIGION Eddie S. Glaude JrAFRICAN HISTORY John Parker and Richard RathboneAFRICAN POLITICS Ian TaylorAFRICAN RELIGIONS Jacob K. OluponaAGEING Nancy A. PachanaAGNOSTICISM Robin Le PoidevinAGRICULTURE Paul Brassley and Richard SoffeALEXANDER THE GREAT Hugh BowdenALGEBRA Peter M. HigginsAMERICAN CULTURAL HISTORY Eric AvilaAMERICAN FOREIGN RELATIONS Andrew PrestonAMERICAN HISTORY Paul S. BoyerAMERICAN IMMIGRATION David A. GerberAMERICAN LEGAL HISTORY G. Edward WhiteAMERICAN NAVAL HISTORY Craig L. SymondsAMERICAN POLITICAL HISTORY Donald CritchlowAMERICAN POLITICAL PARTIES AND ELECTIONS L. Sandy MaiselAMERICAN POLITICS Richard M. ValellyTHE AMERICAN PRESIDENCY Charles O. JonesTHE AMERICAN REVOLUTION Robert J. AllisonAMERICAN SLAVERY Heather Andrea WilliamsTHE AMERICAN WEST Stephen AronAMERICAN WOMEN’S HISTORY Susan WareANAESTHESIA Aidan O’DonnellANALYTIC PHILOSOPHY Michael BeaneyANARCHISM Colin WardANCIENT ASSYRIA Karen RadnerANCIENT EGYPT Ian ShawANCIENT EGYPTIAN ART AND ARCHITECTURE Christina RiggsANCIENT GREECE Paul CartledgeTHE ANCIENT NEAR EAST Amanda H. PodanyANCIENT PHILOSOPHY Julia AnnasANCIENT WARFARE Harry SidebottomANGELS David Albert JonesANGLICANISM Mark ChapmanTHE ANGLO-SAXON AGE John BlairANIMAL BEHAVIOUR Tristram D. WyattTHE ANIMAL KINGDOM Peter HollandANIMAL RIGHTS David DeGraziaTHE ANTARCTIC Klaus DoddsANTHROPOCENE Erle C. EllisANTISEMITISM Steven BellerANXIETY Daniel Freeman and Jason FreemanTHE APOCRYPHAL GOSPELS Paul FosterAPPLIED MATHEMATICS Alain GorielyARCHAEOLOGY Paul BahnARCHITECTURE Andrew BallantyneARISTOCRACY William DoyleARISTOTLE Jonathan BarnesART HISTORY Dana ArnoldART THEORY Cynthia Freeland
ARTIFICIAL INTELLIGENCE Margaret A. BodenASIAN AMERICAN HISTORY Madeline Y. HsuASTROBIOLOGY David C. CatlingASTROPHYSICS James BinneyATHEISM Julian BagginiTHE ATMOSPHERE Paul I. PalmerAUGUSTINE Henry ChadwickAUSTRALIA Kenneth MorganAUTISM Uta FrithAUTOBIOGRAPHY Laura MarcusTHE AVANT GARDE David CottingtonTHE AZTECS Davíd CarrascoBABYLONIA Trevor BryceBACTERIA Sebastian G. B. AmyesBANKING John Goddard and John O. S. WilsonBARTHES Jonathan CullerTHE BEATS David SterrittBEAUTY Roger ScrutonBEHAVIOURAL ECONOMICS Michelle BaddeleyBESTSELLERS John SutherlandTHE BIBLE John RichesBIBLICAL ARCHAEOLOGY Eric H. ClineBIG DATA Dawn E. HolmesBIOGRAPHY Hermione LeeBIOMETRICS Michael FairhurstBLACK HOLES Katherine BlundellBLOOD Chris CooperTHE BLUES Elijah WaldTHE BODY Chris ShillingTHE BOOK OF COMMON PRAYER Brian CummingsTHE BOOK OF MORMON Terryl GivensBORDERS Alexander C. Diener and Joshua HagenTHE BRAIN Michael O’SheaBRANDING Robert JonesTHE BRICS Andrew F. CooperTHE BRITISH CONSTITUTION Martin LoughlinTHE BRITISH EMPIRE Ashley JacksonBRITISH POLITICS Anthony WrightBUDDHA Michael CarrithersBUDDHISM Damien KeownBUDDHIST ETHICS Damien KeownBYZANTIUM Peter SarrisC. S. LEWIS James ComoCALVINISM Jon BalserakCANCER Nicholas JamesCAPITALISM James FulcherCATHOLICISM Gerald O’CollinsCAUSATION Stephen Mumford and Rani Lill AnjumTHE CELL Terence Allen and Graham CowlingTHE CELTS Barry CunliffeCHAOS Leonard SmithCHARLES DICKENS Jenny HartleyCHEMISTRY Peter AtkinsCHILD PSYCHOLOGY Usha GoswamiCHILDREN’S LITERATURE Kimberley ReynoldsCHINESE LITERATURE Sabina KnightCHOICE THEORY Michael AllinghamCHRISTIAN ART Beth WilliamsonCHRISTIAN ETHICS D. Stephen LongCHRISTIANITY Linda WoodheadCIRCADIAN RHYTHMS Russell Foster and Leon KreitzmanCITIZENSHIP Richard BellamyCIVIL ENGINEERING David Muir WoodCLASSICAL LITERATURE William AllanCLASSICAL MYTHOLOGY Helen MoralesCLASSICS Mary Beard and John HendersonCLAUSEWITZ Michael HowardCLIMATE Mark MaslinCLIMATE CHANGE Mark MaslinCLINICAL PSYCHOLOGY Susan Llewelyn and Katie Aafjes-van DoornCOGNITIVE NEUROSCIENCE Richard Passingham
THE COLD WAR Robert McMahonCOLONIAL AMERICA Alan TaylorCOLONIAL LATIN AMERICAN LITERATURE Rolena AdornoCOMBINATORICS Robin WilsonCOMEDY Matthew BevisCOMMUNISM Leslie HolmesCOMPARATIVE LITERATURE Ben HutchinsonCOMPLEXITY John H. HollandTHE COMPUTER Darrel InceCOMPUTER SCIENCE Subrata DasguptaCONCENTRATION CAMPS Dan StoneCONFUCIANISM Daniel K. GardnerTHE CONQUISTADORS Matthew Restall and Felipe Fernández-ArmestoCONSCIENCE Paul StrohmCONSCIOUSNESS Susan BlackmoreCONTEMPORARY ART Julian StallabrassCONTEMPORARY FICTION Robert EaglestoneCONTINENTAL PHILOSOPHY Simon CritchleyCOPERNICUS Owen GingerichCORAL REEFS Charles SheppardCORPORATE SOCIAL RESPONSIBILITY Jeremy MoonCORRUPTION Leslie HolmesCOSMOLOGY Peter ColesCOUNTRY MUSIC Richard CarlinCRIME FICTION Richard BradfordCRIMINAL JUSTICE Julian V. RobertsCRIMINOLOGY Tim NewburnCRITICAL THEORY Stephen Eric BronnerTHE CRUSADES Christopher TyermanCRYPTOGRAPHY Fred Piper and Sean MurphyCRYSTALLOGRAPHY A. M. GlazerTHE CULTURAL REVOLUTION Richard Curt KrausDADA AND SURREALISM David HopkinsDANTE Peter Hainsworth and David RobeyDARWIN Jonathan HowardTHE DEAD SEA SCROLLS Timothy H. LimDECADENCE David WeirDECOLONIZATION Dane KennedyDEMOCRACY Bernard CrickDEMOGRAPHY Sarah HarperDEPRESSION Jan Scott and Mary Jane TacchiDERRIDA Simon GlendinningDESCARTES Tom SorellDESERTS Nick MiddletonDESIGN John HeskettDEVELOPMENT Ian GoldinDEVELOPMENTAL BIOLOGY Lewis WolpertTHE DEVIL Darren OldridgeDIASPORA Kevin KennyDICTIONARIES Lynda MugglestoneDINOSAURS David NormanDIPLOMACY Joseph M. SiracusaDOCUMENTARY FILM Patricia AufderheideDREAMING J. Allan HobsonDRUGS Les IversenDRUIDS Barry CunliffeDYNASTY Jeroen DuindamDYSLEXIA Margaret J. SnowlingEARLY MUSIC Thomas Forrest KellyTHE EARTH Martin RedfernEARTH SYSTEM SCIENCE Tim LentonECONOMICS Partha DasguptaEDUCATION Gary ThomasEGYPTIAN MYTH Geraldine PinchEIGHTEENTH‑CENTURY BRITAIN Paul LangfordTHE ELEMENTS Philip BallEMOTION Dylan EvansEMPIRE Stephen HoweENERGY SYSTEMS Nick JenkinsENGELS Terrell CarverENGINEERING David Blockley
THE ENGLISH LANGUAGE Simon HorobinENGLISH LITERATURE Jonathan BateTHE ENLIGHTENMENT John RobertsonENTREPRENEURSHIP Paul Westhead and Mike WrightENVIRONMENTAL ECONOMICS Stephen SmithENVIRONMENTAL ETHICS Robin AttfieldENVIRONMENTAL LAW Elizabeth FisherENVIRONMENTAL POLITICS Andrew DobsonEPICUREANISM Catherine WilsonEPIDEMIOLOGY Rodolfo SaracciETHICS Simon BlackburnETHNOMUSICOLOGY Timothy RiceTHE ETRUSCANS Christopher SmithEUGENICS Philippa LevineTHE EUROPEAN UNION Simon Usherwood and John PinderEUROPEAN UNION LAW Anthony ArnullEVOLUTION Brian and Deborah CharlesworthEXISTENTIALISM Thomas FlynnEXPLORATION Stewart A. WeaverEXTINCTION Paul B. WignallTHE EYE Michael LandFAIRY TALE Marina WarnerFAMILY LAW Jonathan HerringFASCISM Kevin PassmoreFASHION Rebecca ArnoldFEDERALISM Mark J. Rozell and Clyde WilcoxFEMINISM Margaret WaltersFILM Michael WoodFILM MUSIC Kathryn KalinakFILM NOIR James NaremoreTHE FIRST WORLD WAR Michael HowardFOLK MUSIC Mark SlobinFOOD John KrebsFORENSIC PSYCHOLOGY David CanterFORENSIC SCIENCE Jim FraserFORESTS Jaboury GhazoulFOSSILS Keith ThomsonFOUCAULT Gary GuttingTHE FOUNDING FATHERS R. B. BernsteinFRACTALS Kenneth FalconerFREE SPEECH Nigel WarburtonFREE WILL Thomas PinkFREEMASONRY Andreas ÖnnerforsFRENCH LITERATURE John D. LyonsTHE FRENCH REVOLUTION William DoyleFREUD Anthony StorrFUNDAMENTALISM Malise RuthvenFUNGI Nicholas P. MoneyTHE FUTURE Jennifer M. GidleyGALAXIES John GribbinGALILEO Stillman DrakeGAME THEORY Ken BinmoreGANDHI Bhikhu ParekhGARDEN HISTORY Gordon CampbellGENES Jonathan SlackGENIUS Andrew RobinsonGENOMICS John ArchibaldGEOFFREY CHAUCER David WallaceGEOGRAPHY JOHN Matthews and David HerbertGEOLOGY Jan ZalasiewiczGEOPHYSICS William LowrieGEOPOLITICS Klaus DoddsGERMAN LITERATURE Nicholas BoyleGERMAN PHILOSOPHY Andrew BowieGLACIATION David J. A. EvansGLOBAL CATASTROPHES Bill McGuireGLOBAL ECONOMIC HISTORY Robert C. AllenGLOBALIZATION Manfred StegerGOD John BowkerGOETHE Ritchie RobertsonTHE GOTHIC Nick Groom
GOVERNANCE Mark BevirGRAVITY Timothy CliftonTHE GREAT DEPRESSION AND THE NEW DEAL Eric RauchwayHABERMAS James Gordon FinlaysonTHE HABSBURG EMPIRE Martyn RadyHAPPINESS Daniel M. HaybronTHE HARLEM RENAISSANCE Cheryl A. WallTHE HEBREW BIBLE AS LITERATURE Tod LinafeltHEGEL Peter SingerHEIDEGGER Michael InwoodTHE HELLENISTIC AGE Peter ThonemannHEREDITY John WallerHERMENEUTICS Jens ZimmermannHERODOTUS Jennifer T. RobertsHIEROGLYPHS Penelope WilsonHINDUISM Kim KnottHISTORY John H. ArnoldTHE HISTORY OF ASTRONOMY Michael HoskinTHE HISTORY OF CHEMISTRY William H. BrockTHE HISTORY OF CHILDHOOD James MartenTHE HISTORY OF CINEMA Geoffrey Nowell-SmithTHE HISTORY OF LIFE Michael BentonTHE HISTORY OF MATHEMATICS Jacqueline StedallTHE HISTORY OF MEDICINE William BynumTHE HISTORY OF PHYSICS J. L. HeilbronTHE HISTORY OF TIME Leofranc Holford‑StrevensHIV AND AIDS Alan WhitesideHOBBES Richard TuckHOLLYWOOD Peter DecherneyTHE HOLY ROMAN EMPIRE Joachim WhaleyHOME Michael Allen FoxHOMER Barbara GraziosiHORMONES Martin LuckHUMAN ANATOMY Leslie KlenermanHUMAN EVOLUTION Bernard WoodHUMAN RIGHTS Andrew ClaphamHUMANISM Stephen LawHUME A. J. AyerHUMOUR Noël CarrollTHE ICE AGE Jamie WoodwardIDENTITY Florian CoulmasIDEOLOGY Michael FreedenTHE IMMUNE SYSTEM Paul KlenermanINDIAN CINEMA Ashish RajadhyakshaINDIAN PHILOSOPHY Sue HamiltonTHE INDUSTRIAL REVOLUTION Robert C. AllenINFECTIOUS DISEASE Marta L. Wayne and Benjamin M. BolkerINFINITY Ian StewartINFORMATION Luciano FloridiINNOVATION Mark Dodgson and David GannINTELLECTUAL PROPERTY Siva VaidhyanathanINTELLIGENCE Ian J. DearyINTERNATIONAL LAW Vaughan LoweINTERNATIONAL MIGRATION Khalid KoserINTERNATIONAL RELATIONS Paul WilkinsonINTERNATIONAL SECURITY Christopher S. BrowningIRAN Ali M. AnsariISLAM Malise RuthvenISLAMIC HISTORY Adam SilversteinISOTOPES Rob EllamITALIAN LITERATURE Peter Hainsworth and David RobeyJESUS Richard BauckhamJEWISH HISTORY David N. MyersJOURNALISM Ian HargreavesJUDAISM Norman SolomonJUNG Anthony StevensKABBALAH Joseph DanKAFKA Ritchie RobertsonKANT Roger ScrutonKEYNES Robert SkidelskyKIERKEGAARD Patrick Gardiner
KNOWLEDGE Jennifer NagelTHE KORAN Michael CookLAKES Warwick F. VincentLANDSCAPE ARCHITECTURE Ian H. ThompsonLANDSCAPES AND GEOMORPHOLOGY Andrew Goudie and Heather VilesLANGUAGES Stephen R. AndersonLATE ANTIQUITY Gillian ClarkLAW Raymond WacksTHE LAWS OF THERMODYNAMICS Peter AtkinsLEADERSHIP Keith GrintLEARNING Mark HaselgroveLEIBNIZ Maria Rosa AntognazzaLEO TOLSTOY Liza KnappLIBERALISM Michael FreedenLIGHT Ian WalmsleyLINCOLN Allen C. GuelzoLINGUISTICS Peter MatthewsLITERARY THEORY Jonathan CullerLOCKE John DunnLOGIC Graham PriestLOVE Ronald de SousaMACHIAVELLI Quentin SkinnerMADNESS Andrew ScullMAGIC Owen DaviesMAGNA CARTA Nicholas VincentMAGNETISM Stephen BlundellMALTHUS Donald WinchMAMMALS T. S. KempMANAGEMENT John HendryMAO Delia DavinMARINE BIOLOGY Philip V. MladenovTHE MARQUIS DE SADE John PhillipsMARTIN LUTHER Scott H. HendrixMARTYRDOM Jolyon MitchellMARX Peter SingerMATERIALS Christopher HallMATHEMATICAL FINANCE Mark H. A. DavisMATHEMATICS Timothy GowersMATTER Geoff CottrellTHE MEANING OF LIFE Terry EagletonMEASUREMENT David HandMEDICAL ETHICS Michael Dunn and Tony HopeMEDICAL LAW Charles FosterMEDIEVAL BRITAIN John Gillingham and Ralph A. GriffithsMEDIEVAL LITERATURE Elaine TreharneMEDIEVAL PHILOSOPHY John MarenbonMEMORY Jonathan K. FosterMETAPHYSICS Stephen MumfordMETHODISM William J. AbrahamTHE MEXICAN REVOLUTION Alan KnightMICHAEL FARADAY Frank A. J. L. JamesMICROBIOLOGY Nicholas P. MoneyMICROECONOMICS Avinash DixitMICROSCOPY Terence AllenTHE MIDDLE AGES Miri RubinMILITARY JUSTICE Eugene R. FidellMILITARY STRATEGY Antulio J. Echevarria IIMINERALS David VaughanMIRACLES Yujin NagasawaMODERN ARCHITECTURE Adam SharrMODERN ART David CottingtonMODERN CHINA Rana MitterMODERN DRAMA Kirsten E. Shepherd-BarrMODERN FRANCE Vanessa R. SchwartzMODERN INDIA Craig JeffreyMODERN IRELAND Senia PašetaMODERN ITALY Anna Cento BullMODERN JAPAN Christopher Goto-JonesMODERN LATIN AMERICAN LITERATURE Roberto González EchevarríaMODERN WAR Richard EnglishMODERNISM Christopher Butler
MOLECULAR BIOLOGY Aysha Divan and Janice A. RoydsMOLECULES Philip BallMONASTICISM Stephen J. DavisTHE MONGOLS Morris RossabiMOONS David A. RotheryMORMONISM Richard Lyman BushmanMOUNTAINS Martin F. PriceMUHAMMAD Jonathan A. C. BrownMULTICULTURALISM Ali RattansiMULTILINGUALISM John C. MaherMUSIC Nicholas CookMYTH Robert A. SegalNAPOLEON David BellTHE NAPOLEONIC WARS Mike RapportNATIONALISM Steven GrosbyNATIVE AMERICAN LITERATURE Sean TeutonNAVIGATION Jim BennettNAZI GERMANY Jane CaplanNELSON MANDELA Elleke BoehmerNEOLIBERALISM Manfred Steger and Ravi RoyNETWORKS Guido Caldarelli and Michele CatanzaroTHE NEW TESTAMENT Luke Timothy JohnsonTHE NEW TESTAMENT AS LITERATURE Kyle KeeferNEWTON Robert IliffeNIETZSCHE Michael TannerNINETEENTH‑CENTURY BRITAIN Christopher Harvie and H. C. G. MatthewTHE NORMAN CONQUEST George GarnettNORTH AMERICAN INDIANS Theda Perdue and Michael D. GreenNORTHERN IRELAND Marc MulhollandNOTHING Frank CloseNUCLEAR PHYSICS Frank CloseNUCLEAR POWER Maxwell IrvineNUCLEAR WEAPONS Joseph M. SiracusaNUMBERS Peter M. HigginsNUTRITION David A. BenderOBJECTIVITY Stephen GaukrogerOCEANS Dorrik StowTHE OLD TESTAMENT Michael D. CooganTHE ORCHESTRA D. Kern HolomanORGANIC CHEMISTRY Graham PatrickORGANIZATIONS Mary Jo HatchORGANIZED CRIME Georgios A. Antonopoulos and Georgios PapanicolaouORTHODOX CHRISTIANITY A. Edward SiecienskiPAGANISM Owen DaviesPAIN Rob BoddiceTHE PALESTINIAN-ISRAELI CONFLICT Martin BuntonPANDEMICS Christian W. McMillenPARTICLE PHYSICS Frank ClosePAUL E. P. SandersPEACE Oliver P. RichmondPENTECOSTALISM William K. KayPERCEPTION Brian RogersTHE PERIODIC TABLE Eric R. ScerriPHILOSOPHY Edward CraigPHILOSOPHY IN THE ISLAMIC WORLD Peter AdamsonPHILOSOPHY OF BIOLOGY Samir OkashaPHILOSOPHY OF LAW Raymond WacksPHILOSOPHY OF SCIENCE Samir OkashaPHILOSOPHY OF RELIGION Tim BaynePHOTOGRAPHY Steve EdwardsPHYSICAL CHEMISTRY Peter AtkinsPHYSICS Sidney PerkowitzPILGRIMAGE Ian ReaderPLAGUE Paul SlackPLANETS David A. RotheryPLANTS Timothy WalkerPLATE TECTONICS Peter MolnarPLATO Julia AnnasPOETRY Bernard O’DonoghuePOLITICAL PHILOSOPHY David MillerPOLITICS Kenneth Minogue
POPULISM Cas Mudde and Cristóbal Rovira KaltwasserPOSTCOLONIALISM Robert YoungPOSTMODERNISM Christopher ButlerPOSTSTRUCTURALISM Catherine BelseyPOVERTY Philip N. JeffersonPREHISTORY Chris GosdenPRESOCRATIC PHILOSOPHY Catherine OsbornePRIVACY Raymond WacksPROBABILITY John HaighPROGRESSIVISM Walter NugentPROJECTS Andrew DaviesPROTESTANTISM Mark A. NollPSYCHIATRY Tom BurnsPSYCHOANALYSIS Daniel PickPSYCHOLOGY Gillian Butler and Freda McManusPSYCHOLOGY OF MUSIC Elizabeth Hellmuth MargulisPSYCHOPATHY Essi VidingPSYCHOTHERAPY Tom Burns and Eva Burns-LundgrenPUBLIC ADMINISTRATION Stella Z. Theodoulou and Ravi K. RoyPUBLIC HEALTH Virginia BerridgePURITANISM Francis J. BremerTHE QUAKERS Pink DandelionQUANTUM THEORY John PolkinghorneRACISM Ali RattansiRADIOACTIVITY Claudio TunizRASTAFARI Ennis B. EdmondsREADING Belinda JackTHE REAGAN REVOLUTION Gil TroyREALITY Jan WesterhoffTHE REFORMATION Peter MarshallRELATIVITY Russell StannardRELIGION IN AMERICA Timothy BealTHE RENAISSANCE Jerry BrottonRENAISSANCE ART Geraldine A. JohnsonREPTILES T. S. KempREVOLUTIONS Jack A. GoldstoneRHETORIC Richard ToyeRISK Baruch Fischhoff and John KadvanyRITUAL Barry StephensonRIVERS Nick MiddletonROBOTICS Alan WinfieldROCKS Jan ZalasiewiczROMAN BRITAIN Peter SalwayTHE ROMAN EMPIRE Christopher KellyTHE ROMAN REPUBLIC David M. GwynnROMANTICISM Michael FerberROUSSEAU Robert WoklerRUSSELL A. C. GraylingRUSSIAN HISTORY Geoffrey HoskingRUSSIAN LITERATURE Catriona KellyTHE RUSSIAN REVOLUTION S. A. SmithTHE SAINTS Simon YarrowSAVANNAS Peter A. FurleySCEPTICISM Duncan PritchardSCHIZOPHRENIA Chris Frith and Eve JohnstoneSCHOPENHAUER Christopher JanawaySCIENCE AND RELIGION Thomas DixonSCIENCE FICTION David SeedTHE SCIENTIFIC REVOLUTION Lawrence M. PrincipeSCOTLAND Rab HoustonSECULARISM Andrew CopsonSEXUAL SELECTION Marlene Zuk and Leigh W. SimmonsSEXUALITY Véronique MottierSHAKESPEARE’S COMEDIES Bart van EsSHAKESPEARE’S SONNETS AND POEMS Jonathan F. S. PostSHAKESPEARE’S TRAGEDIES Stanley WellsSIKHISM Eleanor NesbittTHE SILK ROAD James A. MillwardSLANG Jonathon GreenSLEEP Steven W. Lockley and Russell G. FosterSOCIAL AND CULTURAL ANTHROPOLOGY John Monaghan and Peter Just
SOCIAL PSYCHOLOGY Richard J. CrispSOCIAL WORK Sally Holland and Jonathan ScourfieldSOCIALISM Michael NewmanSOCIOLINGUISTICS John EdwardsSOCIOLOGY Steve BruceSOCRATES C. C. W. TaylorSOUND Mike GoldsmithSOUTHEAST ASIA James R. RushTHE SOVIET UNION Stephen LovellTHE SPANISH CIVIL WAR Helen GrahamSPANISH LITERATURE Jo LabanyiSPINOZA Roger ScrutonSPIRITUALITY Philip SheldrakeSPORT Mike CroninSTARS Andrew KingStatistics David J. HandSTEM CELLS Jonathan SlackSTOICISM Brad InwoodSTRUCTURAL ENGINEERING David BlockleySTUART BRITAIN John MorrillSUPERCONDUCTIVITY Stephen BlundellSYMMETRY Ian StewartSYNAESTHESIA Julia SimnerSYNTHETIC BIOLOGY Jamie A. DaviesTAXATION Stephen SmithTEETH Peter S. UngarTELESCOPES Geoff CottrellTERRORISM Charles TownshendTHEATRE Marvin CarlsonTHEOLOGY David F. FordTHINKING AND REASONING Jonathan St B. T. EvansTHOMAS AQUINAS Fergus KerrTHOUGHT Tim BayneTIBETAN BUDDHISM Matthew T. KapsteinTIDES David George Bowers and Emyr Martyn RobertsTOCQUEVILLE Harvey C. MansfieldTOPOLOGY Richard EarlTRAGEDY Adrian PooleTRANSLATION Matthew ReynoldsTHE TREATY OF VERSAILLES Michael S. NeibergTHE TROJAN WAR Eric H. ClineTRUST Katherine HawleyTHE TUDORS John GuyTWENTIETH‑CENTURY BRITAIN Kenneth O. MorganTYPOGRAPHY Paul LunaTHE UNITED NATIONS Jussi M. HanhimäkiUNIVERSITIES AND COLLEGES David Palfreyman and Paul TempleTHE U.S. CONGRESS Donald A. RitchieTHE U.S. CONSTITUTION David J. BodenhamerTHE U.S. SUPREME COURT Linda GreenhouseUTILITARIANISM Katarzyna de Lazari-Radek and Peter SingerUTOPIANISM Lyman Tower SargentVETERINARY SCIENCE James YeatesTHE VIKINGS Julian D. RichardsVIRUSES Dorothy H. CrawfordVOLTAIRE Nicholas CronkWAR AND TECHNOLOGY Alex RolandWATER John FinneyWAVES Mike GoldsmithWEATHER Storm DunlopTHE WELFARE STATE David GarlandWILLIAM SHAKESPEARE Stanley WellsWITCHCRAFT Malcolm GaskillWITTGENSTEIN A. C. GraylingWORK Stephen FinemanWORLD MUSIC Philip BohlmanTHE WORLD TRADE ORGANIZATION Amrita NarlikarWORLD WAR II Gerhard L. WeinbergWRITING AND SCRIPT Andrew RobinsonZIONISM Michael Stanislawski
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Richard EarlTOPOLOGYA Very Short Introduction
Great Clarendon Street, Oxford, OX2 6DP, United KingdomOxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence inresearch, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford UniversityPress in the UK and in certain other countries Richard Earl 2019The moral rights of the author have been assertedFirst edition published in 2019Impression: 1All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any formor by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, bylicence or under terms agreed with the appropriate reprographics rights organizati
VERY SHORT INTRODUCTIONS are for anyone wanting a stimulating and accessible way into a new subject. They are written by experts, and have been translated into more than 45 different languages. The series began in 1995, and now covers a wide variety of topics in every discipline. The VSI library currently contains over 600 volumes—a Very Short Introduction to everything from Psychology and .
1 Introduction to Combinatorial Algebraic Topology Basic Topology Graphs to Simplicial Complexes Posets to Simplicial Complexes 2 Permutation Patterns Introduction and Motivation Applying Combinatorial Algebraic Topology Kozlov, Dimitry. Combinatorial algebraic topology. Vol. 21. Springer Science & Business Media, 2008.
TOPOLOGY: NOTES AND PROBLEMS Abstract. These are the notes prepared for the course MTH 304 to be o ered to undergraduate students at IIT Kanpur. Contents 1. Topology of Metric Spaces 1 2. Topological Spaces 3 3. Basis for a Topology 4 4. Topology Generated by a Basis 4 4.1. In nitude of Prime Numbers 6 5. Product Topo
a topology on R, the standard topology on R. Thus the open sets are unions of open intervals. A closed interval [c,d] is then closed in this topology. A half-open interval ]a,b],a bis neither open nor closed for this topology. We shall verify later that and R are the only subsets of R which are both open and closed (see (1.9.1)).
of points with the entire collection often regarded as a space; and combinatorial or algebraic topology, which treats geometrical figures as aggregates of smaller building blocks, just as a wall is a collection of bricks. 1 Of course notions of point set topology are used in combinatorial topology, especially for very general geometric .
in combinatorial topology he needed to prove, which has no counterpart in algebraic topology. Even if the backbone of this course is combinatorial topology, the applications in combina- torics will play a centrale role, for they ultimately remain the true motivation.
(An invitation to combinatorial algebraic topology) Combinatorics and topology of toric arrangements II. Topology of arrangements in the complex torus Emanuele Delucchi (SNSF / Universit e de Fribourg) Toblach/Dobbiaco February 23, 2017
Zvi Rosen Applied Algebraic Topology Notes Vladimir Itskov 1. August 24, 2015 Algebraic topology: take \topology" and get rid of it using combinatorics and algebra. Topological space 7!combinatorial object 7!algebra (a bunch of vector spaces with maps).
structure approach [2] that was applied into topology optimization. From then on, topology optimization had become a more active research field. In recent years, topology optimization theory of continuum structure [3] has developed rap
