#2Need help with part 1, 2, and 3 Exercise 2. 1) If (X,d) is a metric space show that B₁(x,r) is always anopen set for x ¤ X and r ≥ 0.2) Give an example of a metric space such that the closed ball Ba(x,r) isnot an open set for any x € X and r ≥ 0.3) Give an example of a metric space such that some closed ball is anopen subset.

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Answered: Exercise 2. 1) If (X, d) is a metric…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

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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Exercise 2. 1) If (X, d) is a metric space show that B(x,r) is always an open set for x = X and r≥ 0.