Injective function and compact set

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Let $f:Mto N$ be a differentiable function between smooth manifolds. Let $Ksubset M$ be a compact set and $f$ is injective on $K$. Also $Df$ is an isomorphism on $K$. Show that there exists an open set $U$ containing $K$ such that $f$ is injective on $U$.



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    up vote
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    Let $f:Mto N$ be a differentiable function between smooth manifolds. Let $Ksubset M$ be a compact set and $f$ is injective on $K$. Also $Df$ is an isomorphism on $K$. Show that there exists an open set $U$ containing $K$ such that $f$ is injective on $U$.



    Thanks in advance.










    share|cite|improve this question

























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      Let $f:Mto N$ be a differentiable function between smooth manifolds. Let $Ksubset M$ be a compact set and $f$ is injective on $K$. Also $Df$ is an isomorphism on $K$. Show that there exists an open set $U$ containing $K$ such that $f$ is injective on $U$.



      Thanks in advance.










      share|cite|improve this question















      Let $f:Mto N$ be a differentiable function between smooth manifolds. Let $Ksubset M$ be a compact set and $f$ is injective on $K$. Also $Df$ is an isomorphism on $K$. Show that there exists an open set $U$ containing $K$ such that $f$ is injective on $U$.



      Thanks in advance.







      smooth-manifolds






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      edited Sep 10 at 21:05

























      asked Sep 10 at 20:58









      bob

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