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walters
 2 years ago
show that if X and Y are Metric spaces with distances dx and dy then
walters
 2 years ago
show that if X and Y are Metric spaces with distances dx and dy then

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walters
 2 years ago
Best ResponseYou've already chosen the best response.0\[D\left(\begin{matrix}x _{1}\\ y _{1}\end{matrix}\right);\left(\begin{matrix}x _{2} \\ y _{2}\end{matrix}\right)\]=max( \[d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})\])

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0is there a part missing from this question?

walters
 2 years ago
Best ResponseYou've already chosen the best response.0yes dw:1361560088275:dw the brackets

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i 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?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0my guess is that you are asked to show that D IS a metric on the product space, where \[D((x_1,y_1),(x_2,y_2):=\max d_x(x_1,x_2), d_y(y_1,y_2)\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0are you trying to prove that it is a metric?

walters
 2 years ago
Best ResponseYou've already chosen the best response.0i 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0that 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0that 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0so 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
 2 years ago
Best ResponseYou've already chosen the best response.0i 've shown them but it is just that i am not show about the meaning of the question

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0me neither, but that seems to me all it CAN mean
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