Let (X, d) be a metric space and let A, B⊆X be such that A is connected, and A∩B ≠ ∅ and A∩ (X − B) ≠ ∅, prove that A∩∂ (B) ≠ ∅. Where ∂ (B) is the boundary of B.
Let (X, d) be a metric space and let A, B⊆X be such that A is connected, and A∩B ≠ ∅ and A∩ (X − B) ≠ ∅, prove that A∩∂ (B) ≠ ∅. Where ∂ (B) is the boundary of 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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Let (X, d) be a metric space and let A, B⊆X be such that A is connected, and A∩B ≠ ∅ and A∩ (X − B) ≠ ∅, prove that A∩∂ (B) ≠ ∅. Where ∂ (B) is the boundary of B.
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