Suppose A and B be subsets of metric space. Show that if A is compact and B is closed then A + B is closed. (using a finite subcover)

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Q: (a) Prove that the metric space (2,11) is complete,

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A: We will show it by giving example

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Q: 3. Let K,and K, be compact subsets of a metric space X. Show K, U K2 is compact

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Q: (a) Prove that every closed subset S of a compact metric space (M,d) is compact in M.

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Q: the euclidean space R³ is a separable metric space. true or false?

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