prove corollary Corollary 2.53 Let (M, d) be a metric space and K C M. The following statementsare equivalent:(i) K is relatively compact.(ii) K is totally bounded and (K,d) is complete.Corollary 2.54 Let (M, d) be a complete metric space and K C M. The followingstatements are equivalent:(i) K is relatively compact.(ii) K is totally bounded.Proof:excercises.

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Answered: Corollary 2.53 Let (M, d) be a metric…

Elementary Linear Algebra (MindTap Course List)

8th Edition

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Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Corollary 2.53 Let (M, d) be a metric space and K C M. The following statements are equivalent: (i) K is relatively compact. (ii) K is totally bounded and (K,d) is complete.