What does the symbol ⊂⊂ mean? [duplicate]

In some texts (mainly complex analysis or harmonic analysis) I sometimes see the following double subset symbol ⊂⊂ for inclusion relation of two regions, ... MathematicsStackExchangeisaquestionandanswersiteforpeoplestudyingmathatanylevelandprofessionalsinrelatedfields.Itonlytakesaminutetosignup. Signuptojointhiscommunity Anybodycanaskaquestion Anybodycananswer Thebestanswersarevotedupandrisetothetop Home Public Questions Tags Users Unanswered Teams StackOverflowforTeams –Collaborateandshareknowledgewithaprivategroup. CreateafreeTeam WhatisTeams? Teams CreatefreeTeam Teams Q&Aforwork Connectandshareknowledgewithinasinglelocationthatisstructuredandeasytosearch. Learnmore Whatdoesthesymbol$\subset\subset$mean?[duplicate] AskQuestion Asked 8years,1monthago Active 8years,1monthago Viewed 4ktimes 5 1 $\begingroup$ Thisquestionalreadyhasananswerhere: Themeaningofnotation$\subset\subset$incomplexanalysis (1answer) Closed8yearsago. Insometexts(mainlycomplexanalysisorharmonicanalysis)Isometimesseethefollowingdoublesubsetsymbol$\subset\subset$forinclusionrelationoftworegions,e.g.,$\Omega$and$\Omega'$aretworegionsin$\mathbb{C}$suchthat$\Omega\subset\subset\Omega'$.Ineverfiguredoutwhatitmeansexactly;Ialwaysinterpreteditastheclosure$\overline{\Omega}$iscontainedin$\Omega'$(sothatsomenastyboundaryeffectscanbeavoided).Isthatright?Ordoes$\subset\subset$meansomeotherkindofinclusion?Thanks. complex-analysisharmonic-analysis Share Cite Follow askedNov13'13at0:17 4ae1e14ae1e1 76555silverbadges1717bronzebadges $\endgroup$ 1 $\begingroup$ ThisisthefirsttimeIseethis.Formeitisamissprint.Let'swaitforthespecialists. $\endgroup$ – Sigur Nov13'13at0:18 Addacomment  |  1Answer 1 Active Oldest Votes 15 $\begingroup$ Itusually(theonlymeaningI'vecomeacrossyet)meansthat$\Omega$isrelativelycompactin$\Omega'$,sotheclosureof$\Omega$iscompactandcontainedin$\Omega'$. Share Cite Follow answeredNov13'13at0:19 DanielFischerDanielFischer 197k1818goldbadges242242silverbadges364364bronzebadges $\endgroup$ 2 $\begingroup$ $A\subsetX$issaidtoberelativelycompactiftheclosureof$A$iscompact.Now$\Omega\subset\Omega'$isrelativelycompactwouldmeantheclosureof$\Omega$in$\Omega'$iscompact.Thatis$\overline\Omega\cap\Omega'$iscompact.Whydoesitfollowthat$\overline\Omega\subset\Omega'$? $\endgroup$ – HritRoy Nov1'19at10:24 1 $\begingroup$ @HritRoySince$\mathbb{C}$isHausdorff,$\overline{\Omega}\cap\Omega'$beingcompactimpliesitisclosedin$\mathbb{C}$,whence$\overline{\Omega}\subset\overline{\Omega}\cap\Omega'$. $\endgroup$ – DanielFischer Nov1'19at10:29 Addacomment  |  Nottheansweryou'relookingfor?Browseotherquestionstaggedcomplex-analysisharmonic-analysisoraskyourownquestion. FeaturedonMeta ProvidingaJavaScriptAPIforuserscripts Congratulationstothe59sitesthatjustleftBeta 2021ElectionResults:Congratulationstoournewmoderators! Linked 3 Themeaningofnotation$\subset\subset$incomplexanalysis 2 Whatdoesthesymbol$\Subset$mean? Related 9 Problem$13.7$inApostol'sMathematicalAnalysis. 5 Theratio$\frac{u(z_2)}{u(z_1)}$forpositiveharmonicfunctionsisuniformlyboundedoncompactsets 3 HowtoprovetheconverseofCarathéodory'stheorem 2 Theset$\Omega\subset\mathbb{C}$iscompactiffeverysequence$\{z_n\}\subset\Omega$hasasubsequencethatconvergestoapointin$\Omega$ 0 QuasiconformalMappings-DefinitionofModulusofa`Quadrilateral' 1 Variousdefinitionsforabranchoflogarithm 2 UnderstandingtheregularrepresentationofanLCAgroupasa'directintegral' HotNetworkQuestions CanIthrowdynamitefrominsidetheeffectsofsanctuary? WhyareSSLCAsprohibitingdoubledashinthirdandfourthcharacters? Howtoreproduceadiagram,isthereanypackagethatdoesit? TransformIdentityMatrix CananoceanandbeachonlyplanetexistwithanO2breathableatmosphere? Howcouldpearsbeusedasammunition? Firstdaya2022UScongresscouldvotetoshutdownJan6thcommission?Howquicklyaftercouldthecommissionbeeffectivelycurtailedorshutdown? WhyisJWSTLaunchingfromFrenchGuiana? Whyarefenders/mudguardssomuchundervalued? Whatdoes"broadcast"meanhere? Whatdoes"terms"refertointhissentence? Differentoccurencesoftheword'period'inalgebraicgeometry Willmyexperienceintheindustryworkagainstmeatthispoint? parsingjsoninbashwithpipeoperators Convertthedecimaldigitsofastring'sUnicodecodepointstobinary,reinterpretasdecimal,andtakethesum Whenwriting,shouldIdescribeascreaminsteadofhavingthecharacteryellout"Ahhhh!" WhatisthemeaningofLuke3:8? HowtomanagediskspaceforGromacsXTC(trajectory)fileoutput DoesWestVirginiahavehigherliteracyratesthanstateslikeNewYork,CaliforniaandNewJersey? Postdocroommatewithstudent AreEnchantmentPointsofferedforAncientHuntslostforever? Whatdoes"super"intitleoforganpiecesmean? SQLCannotrestoredatabaseonYOUNGERserverversion Promotionwillleavemewithaspare$25k.WhatshouldIputthistowards? morehotquestions Yourprivacy Byclicking“Acceptallcookies”,youagreeStackExchangecanstorecookiesonyourdeviceanddiscloseinformationinaccordancewithourCookiePolicy. Acceptallcookies Customizesettings