Question

Problem 3: Let X be a metric space endowed with the metric d(p, q)=\left\{\begin{array}{ll} 1 & \text { if } p \neq q \\ 0 & \text { if }

p=q \end{array}\right. 1. Prove that all subsets of X are both open and closed. 2. Prove that if X has more than one element,then it is not connected. 3. Prove that the only convergent sequences inX are those that remain constant after a certain term.

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