]rrnrnersfon, Ernb_eddrng arrol ny Whr{n4/+ ErnbedA;nX Theo.crn ,() Irnmersran, bef.lr Le+ M/ N be 'funch'on f 'M -r N d;4ferenilabte rnanifolds, Thcn dn Tggerrg.., ls a whore derivafiv.r- is .r*rJwhere inl ediue. di{ferenf ialc 'TExarn p\c r) s An irnmerslon 13 u map thcr{. br$, ar il * T4,pN in;eclive 2) ErnbEddiag r !Sl3 , A rnap {, rrt *n, ts calaol lePer. i{ the- preimage o'p e'vortd carnpact set in N is comPact in M' An ir,rnmcrSion that i6, in3e ctive- arrd propar is called an gglg4$fl / ,.t n .- t.F \ /ff.tof ,a, dxt ernAead;ng {' lil -: N orn (rnme-r'sion , whrch rnotPs iA \ \hr*.0*orph;call6 onto i"ts \rna6e. (+(u) cs) I lr:poSl"l j ' \* {', ttr -+N \s an embrda['nf r rhan 4(n) is a subrnon'{old ,l N --- o sr o Q" *.o \U2' not \alechva is [n3+clve on tangant spcrc€s ] -{,hoLt is for aL[ Pin[s P e M. Li) *(-f--+---\F.> ^ -tro e \ - . 0n irnrne,rsion o4 g{ . bqt the \rnmercfon is . oot an ernbeddiag . Consider the c,r,t"rvc P. GTr,n) -r fL' deflled 11 p Ltl = ( sin 1t , stnt ) . p is cn inlech've- smoo*h irnmersiofl [bu.out. p'L+) neuer vanishes) . it ?s not an enbedd';ng because ite,inaage ie cornpaut whilg its dorno"v' is not' 6, / u,liiii-s atr it, \ / \tmir poMts ,5o i+ is \ I a closed s"bset cl llt'' I I s*,u if is bcvnded qs I \ ,rff rbg'the- Heine-Bre) , I \ thc'rerrr ,it is q cor\^fac+ , \ subsc/ o{ fu P\alt l[1 ' / @
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
]rrnrnersfon, Ernb_eddrng arrol ny Whr{n4/+ ErnbedA;nX Theo.crn
,() Irnmersran,
bef.lr Le+ M/ N be
'funch'on f 'M -r Nd;4ferenilabte rnanifolds, Thcn dn Tggerrg.., ls a
whore derivafiv.r- is .r*rJwhere inl ediue.di{ferenf ialc