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z{%&Rh8S21qyaY*SI+Q_Fm-fu?k#nT4x#VgSIlfD=g|mHv7?|K!Y~V0Hey7rK)Ed3x z;+g%{h2kvdd|R8KC*LJAbd=AKs{OYT$XKnxjRJ%bmEbNz>!#7*j{pK=B{lW6XW2|p zMNYggaaVCsN?liUSPD#9Un40Fy64iXVf>}BV&_lK4QggrFBKY_G-ogQP~e&R-NA=? z5HnBJ^+dE!n~3{Y0?-fbXxIK{>BL(w@@jsKp&$K3p$xcj!cH7+Xort~3w)g>HuycO zaV@VOR^x(RAr(#4K2Nd17}QW^UK~cSg^9 zRA<)EZMAAmG|A&Cs2}E=w>E0mh!%6GFly&QeC%=FpT|Y00yK2Qu9L*5HUPLCpLvT6 zpB%3(*Ms$r9{w5j&M^s(f@! zRWd%&yFyI?Bb>Jj|C*O!J@OjJznD19x14hwzs)|#^vzoR31KJkpq}SM1)K2Y8eUj^ ziWf6@nA-NqmQs{4D7kf19vH2xN!k3U$_$1a{#UYG1diKIF&4Kip0g@XqC_(O^V;q3 z?r35FX`WlYK#Rt*s2;R*DG(RvWoqM?=v5eKH+Bfz(Vw(Q_8~s+Z&94QG+g+TygAfX z=tRSEJ%48!+-nau+)7DX{&I(Vui(lSZcO)P@ET2nbk|c?+$SRv^z6AXvqcNUp*@2m6ZNksK34UT%Wr zLMVDqtus89>biE2kfb(NjzQX9eP>PF$5X)fhsyV5Y(X=qV;0au?nV>qv7`D!`WqXb zBs;<&JGvP=ff*agmu+XF;6Z1q<8uq5V@IV2OHB5!BW4Jo0eU`658kquGOnfoBfkqZ z*)S{ZCM)k`tD(T@N`h%T0=9ez2~Joj}=rF&g8diKu`hABG7+5D!>ew{*E_AI~w z>-tf)k7-QcefAF4(gbeTl~V(M@@_U!6E?D;8^`bF=du&r$U2_`?v}nz%cAAxA{JH* zzuq}P-;-)PSMVb5O|~DnUWe&EFmFky(tXmlDS^UZ3iIXX;vPj)!>hg_MXO2b_zB?+ zc1A{YK*02#X_Hg2{uJ)Zh+PJ6)SEiz?B1uQi}UvGZ>KM485vQmmHm4TaUDm^<6vCO z?dzmr|A{^99R&y98#^#>&&*!h&baUPH44+ 0$ takové, že pokud $\| (y_0, s_0) - (t_0, x_0) \|$, potom řešení $y$ procházející bodem $(y_0, s_0)$ je definované v bodech $(t - r, t + r)$, spojitost pak odpovídá tomu, že toto řešení bude po celou dobu ``blízko" toho původního. + Intermezzo: otevřenost $G$ znamená, že pro každé $(x_0, t_0) \in \Omega$ a $t$ existuje $r > 0$ takové, že pokud $\| (y_0, s_0) - (x_0, t_0) \|$ je malé, potom řešení $y$ procházející bodem $(y_0, s_0)$ je definované v bodech $(t - r, t + r)$, spojitost pak odpovídá tomu, že toto řešení bude po celou dobu ``blízko" toho původního. Bez újmy na obecnosti nechť $t_0 > t$. Vezměme $(t; t_0, x_0) \in G$, buď $x$ maximální řešení s počáteční podmínkou $x(t_0) = x_0$. Pak $[t_0, t] \subset D_x$ (řešení je definováno na celém tomto intervalu). Vezměme $\delta > 0$ tak malé, aby $[t_0, t + 2\delta] \subset D_x$ (to můžeme, neboť $D_x$ je otevřená) a zároveň $K_\delta := \{ (y, s) \in \mathbb{R}^n \times \mathbb{R} : s \in [t_0 - \delta, t + \delta] \land |y(s) - x(s)| \leq \delta \} \subset \Omega$. Takto definovaná množina $K_\delta$ je kompaktní a tedy $f$ je na $K_\delta$ omezená konstantou $c_0$ (spojitá funkce na kompaktu) díky čemuž z lokální lipschitzovskosti plyne globální $L$-lipschitzovskost vzhledem k $x$.