In a discrete metric space M any open Ball is


A) non empty subset of M

B) empty

C) either a singleton set or the whole space

D) none of these

Correct Answer:
C) either a singleton set or the whole space

Description for Correct answer:
Let \(x\in M\)

Then \(B(x,r)=\{x\}\) if \(r<1\)

\(B(x,r)=M\) if \(r\ge 1\)

Therefore in a discrete metric space M any open ball is either a singleton set or the whole space.

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








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