3. Let Y be the set of compact subsets of R" for some n e N. We define the distance from a point x ER" to a compact subs

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3 Let Y Be The Set Of Compact Subsets Of R For Some N E N We Define The Distance From A Point X Er To A Compact Subs 1 (33.29 KiB) Viewed 34 times

3. Let Y be the set of compact subsets of R" for some n e N. We define the distance from a point x ER" to a compact subset Be Y as dist(x, B) := min{d(x,y) y € B}. For A, B EY we then define dy(A,B) = max{max{dist(x, B) x E A}, max{dist(y, A) ly e B}}. = (a) Show that dy is a metric on Y. (b) Show that this metric is complete. (c) Bonus problem: show the same if R" is replaced by a compact metric space X.