walters
  • walters
show that if X and Y are Metric spaces with distances dx and dy then
Mathematics
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schrodinger
  • schrodinger
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walters
  • walters
\[D\left(\begin{matrix}x _{1}\\ y _{1}\end{matrix}\right);\left(\begin{matrix}x _{2} \\ y _{2}\end{matrix}\right)\]=max( \[d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})\])
walters
  • walters
@saifoo.khan
anonymous
  • anonymous
is there a part missing from this question?

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walters
  • walters
yes |dw:1361560088275:dw| the brackets
anonymous
  • anonymous
i still think there is something missing X and Y are metric spaces, with some metric defined on each what does \((x_1,y_1)\) mean? are you trying to define a metric on the product?
anonymous
  • anonymous
my guess is that you are asked to show that D IS a metric on the product space, where \[D((x_1,y_1),(x_2,y_2):=\max d_x(x_1,x_2), d_y(y_1,y_2)\]
walters
  • walters
|dw:1361560337199:dw|
anonymous
  • anonymous
are you trying to prove that it is a metric?
walters
  • walters
i don't understand wat the question means does it means i have to prove that LHS=RHS or showing that it is the metric space
anonymous
  • anonymous
that is, you are defining the metric on the product as the max of the distances component wise, and you need to check that is satisfies all the axioms of a metric space
anonymous
  • anonymous
that is what i was asking what is the actual question it looks like you have defined a metric, and you want to prove that it is one, that is, that is satisfies the axioms
anonymous
  • anonymous
so for example you need to check that \[D\left((x_1,y_1), (x_2,y_2)\right)=0\iff (x_1,y_1)=(x_2,y_2)\] etc, that is check each axiom
walters
  • walters
i 've shown them but it is just that i am not show about the meaning of the question
anonymous
  • anonymous
me neither, but that seems to me all it CAN mean

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