1. Let d, be a metries on X#o and let the function d: X x XR defined by: da, y) 1+ di(1, 9) Vr. y € X. d(r, y) = prove that (X, d) is a metric space, 2. Determine whether the following subsets of R are the neighborhood of of the point 3 A = (1,5), B = {1,2,3, 4,5), N, Z. Q. 3. In R with the usual metric , find: (i) The interior of (2, 3) U (5, 6) (ii) The interior of (5,6) (iii) The limit point of (2,3) (Iv) The closure of the set (1+ n+1 4. Give an example to show that the equality may not hold in An BC An B.

1. Let d, be a metries on X#o and let the function d: X x XR defined by: da, y) 1+ di(1, 9) Vr. y € X. d(r, y) = prove that (X, d) is a metric space, 2. Determine whether the following subsets of R are the neighborhood of of the point 3 A = (1,5), B = {1,2,3, 4,5), N, Z. Q. 3. In R with the usual metric , find: (i) The interior of (2, 3) U (5, 6) (ii) The interior of (5,6) (iii) The limit point of (2,3) (Iv) The closure of the set (1+ n+1 4. Give an example to show that the equality may not hold in An BC An B.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 49E

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