Injective function and compact set
Clash Royale CLAN TAG#URR8PPP
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.
smooth-manifolds
add a comment |Â
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.
smooth-manifolds
add a comment |Â
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.
smooth-manifolds
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
smooth-manifolds
edited Sep 10 at 21:05
asked Sep 10 at 20:58
bob
527
527
add a comment |Â
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2912351%2finjective-function-and-compact-set%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password