Description
Problem 6 (Exercise 2.14). Give an example of an open cover of the segment (0, 1) which has no finite subcover.
Problem 7 (Exercise 2.18). Is there a nonempty perfect set in R1 which contains no rational number?
Problem 8 (Exercise 2.20). Are closures and interiors of connected sets always connected?
√
Problem 9 (Exercise 3.3). If s1 = 2, and
sn+1 = 2 + √sn (n = 1, 2, 3, . . . ),
prove that {sn} converges, and that sn < 2 for n = 1, 2, 3, . . . .
Problem 10 (Exercise 3.7). Prove that the convergence of an implies the convergence of
√an n
if an ≥ 0.
2
