# Let M be an uncountable discrete metric space. Then M is

Correct Answer: Description for Correct answer:

Let \(A\subset M\) and \(A\ne M\)

Since any set is closed in the discrete metric space M

\(\Rightarrow \overline{A}=A\)

\(\therefore\) A is not dense.

Hence any uncountable discrete metric space is not seprable.

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