Exercise 6.44. Let E be a subset of Rn.(i) Prove that E is closed if and only if it contains all its boundary points.(ii) Prove that E is open if and only if it contains no boundary points.

This is a question of Topology.

Answered: Exercise 6.44. Let E be a subset of Rn.…

Linear Algebra: A Modern Introduction

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ISBN:9781285463247

Author:David Poole

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Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 14EQ

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Exercise 6.44. Let E be a subset of Rn. (i) Prove that E is closed if and only if it contains all its boundary points. (ii) Prove that E is open if and only if it contains no boundary points.