From 05a8aacfe625e587b2effaa813cac59380c2dbd4 Mon Sep 17 00:00:00 2001 From: Semyon Savkin Date: Wed, 16 Jun 2021 01:08:49 +0300 Subject: [PATCH] fix a typo in the proof of proposition 140 --- Lectures/lecture24.tex | 2 +- main.pdf | Bin 2638090 -> 2252702 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/Lectures/lecture24.tex b/Lectures/lecture24.tex index 032c09d..d807191 100644 --- a/Lectures/lecture24.tex +++ b/Lectures/lecture24.tex @@ -60,7 +60,7 @@ \subsection{Двойственность для линейных отображ Тогда $\ker \varphi$ перейдет в $\ker \varphi^{**}$ (это сразу следует из утверждения~\ref{claim::CanonicalIsomorphism}). Кроме того, $(\Im \varphi^*)^\bot \subseteq V$, где ортогональное дополнение берется относительно формы $V^*\times V\to F$, перейдет в $(\Im \varphi^*)^\bot\subseteq V^{**}$, где ортогональное дополнение берется относительно формы $V^*\times V^{**}\to F$. Это получается из замечания перед формулировкой утверждения выше. -Потому нам достаточно показать, что $(\Im \varphi^*)^\bot = \ker(\varphi^*)^*$ в пространстве $V^{**}$. +Потому нам достаточно показать, что $(\Im \varphi^*)^\bot = \ker(\varphi^{**})$ в пространстве $V^{**}$. А это равносильно (1), примененному к отображению $\varphi^*\colon U^*\to V^*$. \end{proof} diff --git a/main.pdf b/main.pdf index 9084bf11214537259d80f719aedbb9b05fa1c6d1..36ad09bce00faba6575e3a85016c09fea29cc483 100644 GIT binary patch delta 736616 zcmZ^~Q;;S=v$flpwr$(Cd)l^b+j`r!ZA{y?ZEM=L-F@cU2Yc^`|3uV9*1D>T%y=qS zRYnFD0O$5b0E?0-h=|cK(X&C5%`FYDK{FFF651PCLG$uLGpKkvm=ZF`8(As4*g`YN z5i&6{LNkb2Iyt)#aX7=i6O?KqFC5CJcitZL*40W>IMxDf<=EZ3wf6R>%oi8;QF6M0*SB};T&Nm7bsUD$WTE( zX&%+k7!)@Oxf+PyufSwd{W?YWPsxDD;Xw}}-#|=4$$$yqXdJXLkO{|r4{%;f8AR9t zfF*f2Go_{;h-$(;%Puwe3|}P7G#^r*=^~IWlO!+Vs}y}DEMel{AI(zK2CjexR0HZ? zGlG07p~(t?4W|7PjklT8OCU-MBqQtoLU@91KKaqHPj$$VSZ3gJs4O$tL|`Fp6EK9P z?1c~ODi3Hwys^K8od}Kzo!S}9#868u0W6X-KChqaKJW8B?|T>W`qO1M(_sRBUq`b$ zJ>TC6dQ)i(VFf_&nA!5tM;ARzpdDjFBZ!H zFM&7$wF96eXK#FQ`s#~loJh~J61C6TJdEw1iwz8?bt50Gm@qW&p4BHGt!ThCK!8s_ z)}2S63c>wQEXA;|ejKgrJdF`cZ<(_t1wL-d=bsd1Z9EFyxU=i)U zbPv8AmGb`JeMzzLp4viGRZnZv*;GxV-XdsP6~Z^`-h31&T@YJseV2Wa-R-*V?4_Xmz(1?z5whewp 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