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

1. walters Group Title

$D\left(\begin{matrix}x _{1}\\ y _{1}\end{matrix}\right);\left(\begin{matrix}x _{2} \\ y _{2}\end{matrix}\right)$=max( $d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})$)

2. walters Group Title

@saifoo.khan

3. satellite73 Group Title

is there a part missing from this question?

4. walters Group Title

yes |dw:1361560088275:dw| the brackets

5. satellite73 Group Title

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 Group Title

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 Group Title

|dw:1361560337199:dw|

8. satellite73 Group Title

are you trying to prove that it is a metric?

9. walters Group Title

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 Group Title

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 Group Title

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 Group Title

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 Group Title

i 've shown them but it is just that i am not show about the meaning of the question

14. satellite73 Group Title

me neither, but that seems to me all it CAN mean