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


A) separable

B) not separable

C) empty

D) none of these

Correct Answer:
A) separable

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.

Part of solved Real Analysis questions and answers : >> Elementary Mathematics >> Real Analysis








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