Mixing
Injective map that is not an immersion
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I am studying analysis and I have had a lot of uncertainties. For instance, I cannot solve this exercise:
If $f:UrightarrowmathbbR^3$ has class $C^1$ and rank $3$ in all of the points of the open $UinmathbbR^4$, show that $|f(x)|$ do not assume maximal value for $xin U$.
(I guess this is the comand, but I'm so sorry if I did mistakes. My language and the language of the comand is Portuguese)
Well. I know that $f$ is a submersion. So, it's an open map. From here can I get the required? If I know that $f$ is an open map, have I that $|f(x)|$ is an open set and so that it has not a maximum?
analysis matrix-rank open-map
asked Jul 16 at 18:48
Na'omi
83
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up vote
0
down vote
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I am studying analysis and I have had a lot of uncertainties. For instance, I cannot solve this exercise:
If $f:UrightarrowmathbbR^3$ has class $C^1$ and rank $3$ in all of the points of the open $UinmathbbR^4$, show that $|f(x)|$ do not assume maximal value for $xin U$.
(I guess this is the comand, but I'm so sorry if I did mistakes. My language and the language of the comand is Portuguese)
Well. I know that $f$ is a submersion. So, it's an open map. From here can I get the required? If I know that $f$ is an open map, have I that $|f(x)|$ is an open set and so that it has not a maximum?
analysis matrix-rank open-map
asked Jul 16 at 18:48
Na'omi
83
Your second paragraph makes no sense to me.
– zhw.
Jul 16 at 20:08
Sorry, I did a mistake and I hope now the question is correct. Thanks.
– Na'omi
Jul 16 at 21:52
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am studying analysis and I have had a lot of uncertainties. For instance, I cannot solve this exercise:
If $f:UrightarrowmathbbR^3$ has class $C^1$ and rank $3$ in all of the points of the open $UinmathbbR^4$, show that $|f(x)|$ do not assume maximal value for $xin U$.
(I guess this is the comand, but I'm so sorry if I did mistakes. My language and the language of the comand is Portuguese)
Well. I know that $f$ is a submersion. So, it's an open map. From here can I get the required? If I know that $f$ is an open map, have I that $|f(x)|$ is an open set and so that it has not a maximum?
analysis matrix-rank open-map
asked Jul 16 at 18:48
Na'omi
83
I am studying analysis and I have had a lot of uncertainties. For instance, I cannot solve this exercise:
If $f:UrightarrowmathbbR^3$ has class $C^1$ and rank $3$ in all of the points of the open $UinmathbbR^4$, show that $|f(x)|$ do not assume maximal value for $xin U$.
(I guess this is the comand, but I'm so sorry if I did mistakes. My language and the language of the comand is Portuguese)
Well. I know that $f$ is a submersion. So, it's an open map. From here can I get the required? If I know that $f$ is an open map, have I that $|f(x)|$ is an open set and so that it has not a maximum?
analysis matrix-rank open-map
asked Jul 16 at 18:48
Na'omi
83
edited Jul 17 at 0:14
asked Jul 16 at 18:48
Na'omi
83
asked Jul 16 at 18:48
Na'omi
83
asked Jul 16 at 18:48
Na'omi
83
83
Your second paragraph makes no sense to me.
– zhw.
Jul 16 at 20:08
Sorry, I did a mistake and I hope now the question is correct. Thanks.
– Na'omi
Jul 16 at 21:52
add a comment |Â
Your second paragraph makes no sense to me.
– zhw.
Jul 16 at 20:08
Sorry, I did a mistake and I hope now the question is correct. Thanks.
– Na'omi
Jul 16 at 21:52
Your second paragraph makes no sense to me.
– zhw.
Jul 16 at 20:08
Your second paragraph makes no sense to me.
– zhw.
Jul 16 at 20:08
Sorry, I did a mistake and I hope now the question is correct. Thanks.
– Na'omi
Jul 16 at 21:52
Sorry, I did a mistake and I hope now the question is correct. Thanks.
– Na'omi
Jul 16 at 21:52
add a comment |Â
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Your second paragraph makes no sense to me.
– zhw.
Jul 16 at 20:08
Sorry, I did a mistake and I hope now the question is correct. Thanks.
– Na'omi
Jul 16 at 21:52