Question: a) A subset E of X is said to be sequentially compact if and only if every sequence xn E has a convergent subsequence

a) A subset E of X is said to be sequentially compact if and only if every sequence xn ∈ E has a convergent subsequence whose limit belongs to E. Prove that every sequentially compact set is closed and bounded.
b) Prove that R is closed but not sequentially compact.
c) Prove that every closed bounded subset of R is sequentially compact.

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