8. (a) A subset E of R is said to be sequentially compact if and only if
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8.
(a) A subset E of R is said to be sequentially compact if and only if every sequence Xn E E has a convergent subsequence whose limit belongs to E.
Prove that every closed bounded interval is sequentially compact.
(b) Prove that there exist bounded intervals in R which are not sequentially compact.
(c) Prove that there exist closed intervals in R which are not sequentially compact.
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