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show that if X and Y are Metric spaces with distances dx and dy then
 one year ago
 one year ago
show that if X and Y are Metric spaces with distances dx and dy then
 one year ago
 one year ago

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waltersBest 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( \[d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})\])
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
is there a part missing from this question?
 one year ago

waltersBest ResponseYou've already chosen the best response.0
yes dw:1361560088275:dw the brackets
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
my guess is that you are asked to show that D IS a metric on the product space, where \[D((x_1,y_1),(x_2,y_2):=\max d_x(x_1,x_2), d_y(y_1,y_2)\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
are you trying to prove that it is a metric?
 one year ago

waltersBest ResponseYou've already chosen the best response.0
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i 've shown them but it is just that i am not show about the meaning of the question
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
me neither, but that seems to me all it CAN mean
 one year ago
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