### 725 Recommended Exercises

Abbreviations and special notation used in denoting certain exercises:
!
especially important to do thoroughly and carefully
?
not clear if worth doing
NB
note well the result  obtained; no comment on worth doing
--
linked: regard as parts of one exercise (NOTE: 5--7 means 5 and 7 are linked, and says nothing about 6.)
Note that exercises are all together at the end of each chapter, grouped by section number.

[chapter pages
section. #exercises.]

• 1 pp.36--41
1. #all.
2. #18, 19, 20.
3. #7, 8, 10, 12.(b).
4. #NB2, 8, 9, NB{12, 13, 14, 18}.
5. #2.(b), 4, 5, NB{6, 7}, 8, NB11, 15.
• 2 pp.75--84
1. #9(b), 16, 17, 18, 19, 23.
2. #4, 9, 12, 14.
3. #1, 6 !(c), 8 !(b), 14 ?(b), 17, 18, 21, 22.
4. #1, 2, 4, 6, 7, 10, 13, 14, 17, 22(b), 23.
5. #5, 9, NB14, 15, 17, NB18, NB19, 20(b), Hausdorff dimension of Koch Snowflake.
• 3 pp.109--15
1. #3, 5(a), 6, 7.
2. #1, 3, 4, 5, 7, 10, 11.
3. #7, 8, 9, 10.
4. #all!
5. #1, ?2, 3, 4, ?5, 6, 7, ?8, ?9, 11.
• 4 pp.136--42
1. #4, 5, 6, 7, 8, 9.
2. #1, 2, 3, 4, 5, 8, 15, 16.
3. #1, 3, 4(f), 6, 8, ?9, 10, ?15, 19, 21.
4. #2, 4, 8, 9, !10, 11, 12, 16, 17, 18, 19, ?20.
• 5 pp.168--74
1. #2, 3, 6--9--10--11, 13, 14, 15, 16, 18, 19, 20 ,21, 22, 23.
2. #1, 4, 5, 6--7, 9, 12, 15(b), 16, 17, 18(a), Are LE spaces first countable? second countable? separable?
3. #2, 4, 7, 10(b), 12, !14, 15, 16, 17, !18, 20, 21, !22, .
4. #?1, 3, 4, 5, 6, 7, 8.
• 6 pp.192--6
1. #2, 4(c), 5, 6, 7, 10, 12, 13, 14, 17, 18.
2. #2, ?3, 4, 5, 9, 10, 11, 12, 13, 15.
3. #2, 3, 5, 7, 10, 11, 13.
• 7 pp.226--32
1. #2, 3, 4, 6, 7, 9, 11, NB14(b).
2. #+NB1, +NB2, 4, 5(b), 6, 7, 9, ?12.
3. #3, 4(a), 5, 10, 11.
4. #2, 3, +NB4, 5, 7, 11, 12, 13, 15, 18, 20, 21, 26!(b).
5. #?1, 2.
• 8 pp.259--62
1. #1, +NB3, 6, 7, 8, 11, 14, 15.
2. #2, 3, +NB4, NB5, 6, NB7, 9, 10.
3. #4, 5, 6.
4. #2, +NB3, 5, +NB6, 7, 9.
Plus all "implicit exercises" such as those parts of proofs "left to the reader."