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walters

  • one year ago

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

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  1. walters
    • one year ago
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    \[D\left(\begin{matrix}x _{1}\\ y _{1}\end{matrix}\right);\left(\begin{matrix}x _{2} \\ y _{2}\end{matrix}\right)\]=max( \[d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})\])

  2. walters
    • one year ago
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    @saifoo.khan

  3. satellite73
    • one year ago
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    is there a part missing from this question?

  4. walters
    • one year ago
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    yes |dw:1361560088275:dw| the brackets

  5. satellite73
    • one year ago
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    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?

  6. satellite73
    • one year ago
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    my guess is that you are asked to show that D IS a metric on the product space, where \[D((x_1,y_1),(x_2,y_2):=\max d_x(x_1,x_2), d_y(y_1,y_2)\]

  7. walters
    • one year ago
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    |dw:1361560337199:dw|

  8. satellite73
    • one year ago
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    are you trying to prove that it is a metric?

  9. walters
    • one year ago
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    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

  10. satellite73
    • one year ago
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    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

  11. satellite73
    • one year ago
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    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

  12. satellite73
    • one year ago
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    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

  13. walters
    • one year ago
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    i 've shown them but it is just that i am not show about the meaning of the question

  14. satellite73
    • one year ago
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    me neither, but that seems to me all it CAN mean

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