Problem

a) A subset E of R is said to be sequentially compact if and only if every sequence xn ∈ E...

a) A subset E of R is said to be sequentially compact if and only if every sequence xnE 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 that are not sequentially compact.

c) Prove that there exist closed intervals in R that are not sequentially compact.

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Solutions For Problems in Chapter 2.4