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(a) Given the metric space R², d where d is the usual metric defined on R2. Let S C R² be a subset defined by {(x, y) = R²: x² + y² <1, x² + (y − 2)² ≤ 4} (i) Is the set S relatively open or relatively closed in subspace that is the open ball B₁ (0,0)? Justify. (ii) Is the set S relatively open or relatively closed in subspace that is the closed ball B₂(0, 2)? Justify your answer.

(a) Given the metric space R², d where d is the usual metric defined on R2. Let S C R² be a subset defined by {(x, y) = R²: x² + y² <1, x² + (y − 2)² ≤ 4} (i) Is the set S relatively open or relatively closed in subspace that is the open ball B₁ (0,0)? Justify. (ii) Is the set S relatively open or relatively closed in subspace that is the closed ball B₂(0, 2)? Justify your answer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 4AEXP
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(a) Given the metric space R2, d > where d is the usual metric defined on R2. Let S CR² be a subset defined by {(x, y) = R²: x² + y² <1, x² + (y − 2)² ≤ 4} (i) Is the set S relatively open or relatively closed in subspace that is the open ball B₁ (0,0)? Justify. (ii) Is the set S relatively open or relatively closed in subspace that is the closed ball B₂(0, 2)? Justify your answer.
Transcribed Image Text:(a) Given the metric space R2, d > where d is the usual metric defined on R2. Let S CR² be a subset defined by {(x, y) = R²: x² + y² <1, x² + (y − 2)² ≤ 4} (i) Is the set S relatively open or relatively closed in subspace that is the open ball B₁ (0,0)? Justify. (ii) Is the set S relatively open or relatively closed in subspace that is the closed ball B₂(0, 2)? Justify your answer.
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