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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 connected metric space and let A be a connected
subset of X. Assume that the complement of A is the union of two separated sets B and C. Prove that A∪B and A∪C are connected.
Prove also that if A is closed, then so are A ∪ B and A ∪ C.
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