Could you explain how to show 5.4 in easiest possible way(in very detail)? Definition. A topological space X is separable if and only if X has a countable densesubset.Exercise 5.4. Find a separable space that contains a subspace that is not separable inthe subspace topology.

To prove the given statement we use the following definition and theorem. Theorem: Uncountable…

Answered: Exercise 5.4. Find a separable space…

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Exercise 5.4. Find a separable space that contains a subspace that is not separable in the subspace topology. а

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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Could you explain how to show 5.4 in easiest possible way(in very detail)?

Definition. A topological space X is separable if and only if X has a countable dense
subset.
Exercise 5.4. Find a separable space that contains a subspace that is not separable in
the subspace topology.

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