Existence of a surjective map between the two space $X$ and $C([a,b],X)$

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Let $X$ a Hilbert space and $Cleft(left[a,bright],Xright)$ the space of Continuous functions from $left[a,bright]$ into $X$. My question is as follows:
is there exists any surjectif map from $Cleft(left[a,bright],Xright)rightarrow X$.
Thank you for your help!







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    up vote
    -1
    down vote

    favorite












    Let $X$ a Hilbert space and $Cleft(left[a,bright],Xright)$ the space of Continuous functions from $left[a,bright]$ into $X$. My question is as follows:
    is there exists any surjectif map from $Cleft(left[a,bright],Xright)rightarrow X$.
    Thank you for your help!







    share|cite|improve this question






















      up vote
      -1
      down vote

      favorite









      up vote
      -1
      down vote

      favorite











      Let $X$ a Hilbert space and $Cleft(left[a,bright],Xright)$ the space of Continuous functions from $left[a,bright]$ into $X$. My question is as follows:
      is there exists any surjectif map from $Cleft(left[a,bright],Xright)rightarrow X$.
      Thank you for your help!







      share|cite|improve this question












      Let $X$ a Hilbert space and $Cleft(left[a,bright],Xright)$ the space of Continuous functions from $left[a,bright]$ into $X$. My question is as follows:
      is there exists any surjectif map from $Cleft(left[a,bright],Xright)rightarrow X$.
      Thank you for your help!









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 20 at 9:46









      zakaria hamidi

      142




      142




















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          $f to f(a)$ is such a map. Note that given $xin X$ the constant map $f(y)=x$ for all $y$ is an element of $C([a,b],X)$






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          • thank you for your help
            – zakaria hamidi
            Aug 20 at 9:59










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          up vote
          3
          down vote













          $f to f(a)$ is such a map. Note that given $xin X$ the constant map $f(y)=x$ for all $y$ is an element of $C([a,b],X)$






          share|cite|improve this answer




















          • thank you for your help
            – zakaria hamidi
            Aug 20 at 9:59














          up vote
          3
          down vote













          $f to f(a)$ is such a map. Note that given $xin X$ the constant map $f(y)=x$ for all $y$ is an element of $C([a,b],X)$






          share|cite|improve this answer




















          • thank you for your help
            – zakaria hamidi
            Aug 20 at 9:59












          up vote
          3
          down vote










          up vote
          3
          down vote









          $f to f(a)$ is such a map. Note that given $xin X$ the constant map $f(y)=x$ for all $y$ is an element of $C([a,b],X)$






          share|cite|improve this answer












          $f to f(a)$ is such a map. Note that given $xin X$ the constant map $f(y)=x$ for all $y$ is an element of $C([a,b],X)$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 20 at 9:49









          Kavi Rama Murthy

          23.3k2933




          23.3k2933











          • thank you for your help
            – zakaria hamidi
            Aug 20 at 9:59
















          • thank you for your help
            – zakaria hamidi
            Aug 20 at 9:59















          thank you for your help
          – zakaria hamidi
          Aug 20 at 9:59




          thank you for your help
          – zakaria hamidi
          Aug 20 at 9:59












           

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