What is meant by pointwise fixed?

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I did not find a direct definition so I will give the context :




$X$ is compact manifold with boundary. There is no smooth map $f:Xrightarrow partial X$ that leaves $partial X$ pointwise fixed.




Here what is meant by pointwise fixed?

I found that fixed means $f(x)=x$ so pointwise means this must be true for all $x$? I am not sure.




general-topology




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    up vote
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    I did not find a direct definition so I will give the context :




    $X$ is compact manifold with boundary. There is no smooth map $f:Xrightarrow partial X$ that leaves $partial X$ pointwise fixed.




    Here what is meant by pointwise fixed?

    I found that fixed means $f(x)=x$ so pointwise means this must be true for all $x$? I am not sure.




    general-topology




    share|cite|improve this question





















      up vote
      5
      down vote

      favorite









      up vote
      5
      down vote

      favorite











      I did not find a direct definition so I will give the context :




      $X$ is compact manifold with boundary. There is no smooth map $f:Xrightarrow partial X$ that leaves $partial X$ pointwise fixed.




      Here what is meant by pointwise fixed?

      I found that fixed means $f(x)=x$ so pointwise means this must be true for all $x$? I am not sure.




      general-topology




      share|cite|improve this question











      I did not find a direct definition so I will give the context :




      $X$ is compact manifold with boundary. There is no smooth map $f:Xrightarrow partial X$ that leaves $partial X$ pointwise fixed.




      Here what is meant by pointwise fixed?

      I found that fixed means $f(x)=x$ so pointwise means this must be true for all $x$? I am not sure.





      general-topology





      share|cite|improve this question










      share|cite|improve this question




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      asked Jul 15 at 6:42









      mathemather

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          It means that every individual $x in partial X$ is fixed by $f$, i.e. $f(x) = x$ for all $x in partial X$.



          In contrast, fixing $partial X$ "setwise" would mean that $f(x) in partial X$ for all $x in partial X$.






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            up vote
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            down vote



            accepted










            It means that every individual $x in partial X$ is fixed by $f$, i.e. $f(x) = x$ for all $x in partial X$.



            In contrast, fixing $partial X$ "setwise" would mean that $f(x) in partial X$ for all $x in partial X$.






            share|cite|improve this answer

























              up vote
              10
              down vote



              accepted










              It means that every individual $x in partial X$ is fixed by $f$, i.e. $f(x) = x$ for all $x in partial X$.



              In contrast, fixing $partial X$ "setwise" would mean that $f(x) in partial X$ for all $x in partial X$.






              share|cite|improve this answer























                up vote
                10
                down vote



                accepted







                up vote
                10
                down vote



                accepted






                It means that every individual $x in partial X$ is fixed by $f$, i.e. $f(x) = x$ for all $x in partial X$.



                In contrast, fixing $partial X$ "setwise" would mean that $f(x) in partial X$ for all $x in partial X$.






                share|cite|improve this answer













                It means that every individual $x in partial X$ is fixed by $f$, i.e. $f(x) = x$ for all $x in partial X$.



                In contrast, fixing $partial X$ "setwise" would mean that $f(x) in partial X$ for all $x in partial X$.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 15 at 6:45









                Mike Haskel

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