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<Text-field style="Heading 1" layout="Normal"><Font encoding="UTF-8">semicont\303\255nuo,</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">adj.</Font>  <Font bold="true">1.</Font><Font encoding="UTF-8">  (de uma fun\303\247\303\243o de valor real, </Font><Font italic="true">f </Font>) tal que ou <Font italic="true">f</Font> ou <Font italic="true">-f</Font> satisfaz  
    lim<Font subscript="true">y<Font family="MaplePi" encoding="UTF-8">\302\256</Font>x</Font> inf <Font italic="true">f(y)</Font> <Font family="MaplePi" encoding="UTF-8">\302\263</Font> <Font italic="true">f(x)</Font>.  
Se <Font italic="true">f</Font><Font encoding="UTF-8"> por si s\303\263 satisfaz esta condi\303\247\303\243o, ela \303\251 <Font italic="true">semicont\303\255nua abaixo</Font></Font>, e isto corresponde a <Hyperlink linktarget="Dictionary:Definition/levelset" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">level sets</Font></Hyperlink> mais baixos da forma  
    {<Font italic="true">x</Font>: <Font italic="true">f</Font>(<Font italic="true">x</Font>) <Font family="MaplePi" encoding="UTF-8">\302\243</Font> <Font italic="true">r</Font>}   
sendo fechado, ou ao <Hyperlink linktarget="Dictionary:Definition/epigraph" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">epigraph</Font></Hyperlink>   
    {(<Font italic="true">x</Font>, <Font italic="true">r</Font>): <Font italic="true">f</Font>(<Font italic="true">x</Font>) <Font family="MaplePi" encoding="UTF-8">\302\243</Font> <Font italic="true">r</Font>}   
<Font encoding="UTF-8">sendo fechado.  Uma fun\303\247\303\243o</Font><Font italic="true"> f</Font><Font encoding="UTF-8"> \303\251 <Font italic="true">semicont\303\255nua superior</Font></Font> se -<Font italic="true">f</Font><Font encoding="UTF-8"> \303\251 semicont\303\255nua inferior. Uma fun\303\247\303\243o \303\251 cont\303\255nua se, e somente se, ela \303\251 semicont\303\255nua tanto superior como inferior.   </Font><Font bold="true">2.</Font> (de um <Hyperlink linktarget="Dictionary:Definition/set-valuedfunction" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">set-valued function</Font></Hyperlink>) tal que a <Hyperlink linktarget="Dictionary:Definition/inverseimage" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">inverse image</Font></Hyperlink><Font encoding="UTF-8"> superior ou inferior de qualquer conjunto aberto \303\251 aberta; a multifun\303\247\303\243o \303\251, portanto, <Font italic="true">semicont\303\255nua inferior</Font></Font> ou <Font italic="true">superior</Font><Font encoding="UTF-8">, respectivamente.  Uma multifun\303\247\303\243o com ambas as propriedades \303\251 algumas vezes dita ser uma <Font italic="true">multifun\303\247\303\243o cont\303\255nua. </Font>Existem m\303\272ltiplas defini\303\247\303\265es concorrentes para continuidade e semicontinuidade superior, muitas envolvendo </Font><Hyperlink linktarget="Dictionary:Definition/Hausdorffdistance" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">Hausdorff distance</Font></Hyperlink><Font encoding="UTF-8">. Uma multifun\303\247\303\243o entre espa\303\247os compactos que possui imagens fechadas \303\251 semicont\303\255nua superior exatamente se ela possui um gr\303\241fico fechado.  Para uma correspond\303\252ncia de um \303\272nico valor, ambas coincidem individualmente com continuidade.</Font></Text-field>
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