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(Solved): For a metric space \( (X, d) \), and \( A \subset X \), we define the boundary of \( A \) to be the ...
![(c) \( [0,1] \).
(d) \( (0,1) \).
(e) \( \mathbb{Z} \).](https://media.cheggcdn.com/study/623/6237bf3c-9786-4813-b0c2-ca6ada47fa3e/image)
For a metric space \( (X, d) \), and \( A \subset X \), we define the boundary of \( A \) to be the set \( B d r y(A)=\bar{A} \cap \bar{X} \backslash A \)
14. Describe the boundaries of the following subsets of \( \mathbb{R} \). (a) \( \mathbb{Q} \). (b) \( \mathbb{R} \backslash \mathbb{Q} \).
(c) \( [0,1] \). (d) \( (0,1) \). (e) \( \mathbb{Z} \).