Let (X, dX) and (Y, dY) be metric spaces.Define the function d : (X × Y...

Let (X, d_X) and (Y, d_Y) be metric spaces.Define the function

d : (X × Y ) × (X × Y ) → R

by

d ((x₁, y₁), (x₂,y₂)) = d_x(x₁,x₂)+d_y(y₁,y₂)

Prove that d is a metric on X × Y .

Expert Solution

Colby Messinger answered 2 years ago

Suppose (X, dX) and (Y, dY ) are metric spaces. Define d : (X ×Y )×(X...

Suppose (X, dX) and (Y, dY ) are metric spaces. Define d : (X ×Y )×(X × Y ) → R by d((x, y),(a, b)) = dX(x, a) + dY (y, b). Prove d is a metric on X × Y .

Let (X,dX),(Y,dY ) be metric spaces and f: X → Y be a continuous bijection. Prove...

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Euclidean metric) The metric d (( x 1 ,x 2 ) , ( y 1 ,y...

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