how to show two metrics are equivalent and uniformly equivalent?
$begingroup$
I am having some problems with the question attached. I already know the definitions of equivalent and uniformly equivalent metrics but I find this question a bit challenging.
I would really appreciate if you suggest me similar problems as well but not too easy ones.
Here is the question
real-analysis analysis
asked Dec 20 '18 at 9:38
lalalala
11
$endgroup$
add a comment |
$begingroup$
I am having some problems with the question attached. I already know the definitions of equivalent and uniformly equivalent metrics but I find this question a bit challenging.
I would really appreciate if you suggest me similar problems as well but not too easy ones.
Here is the question
real-analysis analysis
asked Dec 20 '18 at 9:38
lalalala
11
$endgroup$
$begingroup$
"the first metric has x and y but the Euclidean has x1 and x2" the notation is irrelevant. If you have $xinmathbb{R}^2$, the coordinates can be named $x_1$ and $x_2$ or $x$ and $y$ or $dog$ and $cat$, or as you like.
$endgroup$
– Martín Vacas Vignolo
Dec 20 '18 at 9:44
add a comment |
$begingroup$
I am having some problems with the question attached. I already know the definitions of equivalent and uniformly equivalent metrics but I find this question a bit challenging.
I would really appreciate if you suggest me similar problems as well but not too easy ones.
Here is the question
real-analysis analysis
asked Dec 20 '18 at 9:38
lalalala
11
$endgroup$
I am having some problems with the question attached. I already know the definitions of equivalent and uniformly equivalent metrics but I find this question a bit challenging.
I would really appreciate if you suggest me similar problems as well but not too easy ones.
Here is the question
real-analysis analysis
real-analysis analysis
asked Dec 20 '18 at 9:38
lalalala
11
asked Dec 20 '18 at 9:38
lalalala
11
edited Dec 20 '18 at 10:40
lala
asked Dec 20 '18 at 9:38
lalalala
11
asked Dec 20 '18 at 9:38
lalalala
11
asked Dec 20 '18 at 9:38
lalalala
11
11
$begingroup$
"the first metric has x and y but the Euclidean has x1 and x2" the notation is irrelevant. If you have $xinmathbb{R}^2$, the coordinates can be named $x_1$ and $x_2$ or $x$ and $y$ or $dog$ and $cat$, or as you like.
$endgroup$
– Martín Vacas Vignolo
Dec 20 '18 at 9:44
add a comment |
$begingroup$
"the first metric has x and y but the Euclidean has x1 and x2" the notation is irrelevant. If you have $xinmathbb{R}^2$, the coordinates can be named $x_1$ and $x_2$ or $x$ and $y$ or $dog$ and $cat$, or as you like.
$endgroup$
– Martín Vacas Vignolo
Dec 20 '18 at 9:44
$begingroup$
"the first metric has x and y but the Euclidean has x1 and x2" the notation is irrelevant. If you have $xinmathbb{R}^2$, the coordinates can be named $x_1$ and $x_2$ or $x$ and $y$ or $dog$ and $cat$, or as you like.
$endgroup$
– Martín Vacas Vignolo
Dec 20 '18 at 9:44
$begingroup$
"the first metric has x and y but the Euclidean has x1 and x2" the notation is irrelevant. If you have $xinmathbb{R}^2$, the coordinates can be named $x_1$ and $x_2$ or $x$ and $y$ or $dog$ and $cat$, or as you like.
$endgroup$
– Martín Vacas Vignolo
Dec 20 '18 at 9:44
add a comment |
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$begingroup$
"the first metric has x and y but the Euclidean has x1 and x2" the notation is irrelevant. If you have $xinmathbb{R}^2$, the coordinates can be named $x_1$ and $x_2$ or $x$ and $y$ or $dog$ and $cat$, or as you like.
$endgroup$
– Martín Vacas Vignolo
Dec 20 '18 at 9:44