Answered: Let (X, d) be a metric space and let A…

Let (X, d) be a metric space and let A ⊆ X be a compact subset. show that, If B ⊆ X and d(A, B) = inf{d(a, b) : a ∈ A and b ∈ B} = 0 then A ∩ B = ∅.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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Question

Let (X, d) be a metric space and let A ⊆ X be a compact subset.

show that,

If B ⊆ X and d(A, B) = inf{d(a, b) : a ∈ A and b ∈ B} = 0 then A ∩

B = ∅.

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