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# 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

 C) either a singleton set or the whole space

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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