Question 1. Given a metric space < X, p>. (a) If x, y E X and p(x, y) < ɛ for all e > 0, prove that x = = y. (b) Prove that a sequence (xn)nEN C X can have at most one limit.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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A: Since you have asked multiple questions, we will answer the first one. If you want other questions…

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A: on solving this we get

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