Let (X, d) be a metric space, x E X, e > 0, and E = {y Ex: d(x, y) ≤ e}. Prove that E is closed.

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Q: 1. Let, y eR. Determine if the following are metrics on R or not (a) d, (x, y) = /1x - y| (b)…

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Q: 4. Let {Ka}aeA be a collection of compact subsets of a metric space, Show NaEA K, is closed

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