Solutions to exercises

This is a list of solutions to exercises in the book Spaces.

Some of these solutions were written for an earlier draft of the book. If an exercise is marked as "X (labeled Y)" then the exercise numbering has changed from Y to X in the printed version of the book.

The exercises are not listed in strictly increasing order, so try to search further down the page if you can't find what you're looking for.

PDF	Exercises
Solutions	Section 1.1: 1, 2, 3, 4 Section 1.2: 1, 2, 5, 6, 9 (labeled 1.2.8) Section 1.3: 1, 2, 3, 4, 5, 6 Section 1.4: 1, 3, 4, 8 (labeled 1.4.7) Section 1.5: 3, 5, 6
Solutions	Some of these are only hints. Section 2.1: 1, 2, 4, 7 Section 2.2: 1�C5 (labeled as 2.1....) (In exercise 2.2.5 it should say \(A_n = \{-1,0,1\}\)) Section 2.2: 9 Section 2.3: 1, 2, 4, 9 Hints for some exercises in Sections 3.1, 3.2
Solutions	Section 1.6: 1, 2, 5 Section 3.1: 1, 2, 3, 6, 7 Section 3.2: 1, 2, 3, 5, 6, 8 (labeled 3.1.8) Section 3.3: 1, 2, 3, 5 (labeled 3.3.4), 6 (labeled 3.3.5)
Solutions	Section 3.3: 4a (labeled 3.3.7 and 3.3.8a), 4b (labeled 3.3.8b), 8 (labeled 3.3.9), 9 (labeled 3.3.10), 11 (labeled 3.3.12), 12 (labeled 3.3.13) Section 3.4: 1, 2, 3, 5, 6, 7, 8 Section 3.5: 1, 2, 3, 4, 6 (labeled 3.5.5), 7 (labeled 3.5.6), 8 (labeled 3.5.7)
Solutions	Section 3.5: 9 (labeled 3.5.8), 13 (labeled 3.5.11), 14 (labeled 3.5.12), 16 (labeled 3.5.14) Section 3.6: 1, 2, 3, 4 Section 4.1: 1, 2, 3, 4
Solutions	Section 4.2: 1, 2, 3, 4, 5, 6, 9, 12 Section 4.3: 1, 5c (labeled 4.3.2), 3, 6 (labeled 4.3.5, and with cos instead of sin) Section 2.2: 4, 7 Section 4.4: 1, 3, 4
Solutions	Section 4.4: 5, 6 (labeled 4.4.7), 7 (labeled 4.4.6) Section 4.5: 1, 2, 3, 5, 6, 7 Section 4.6: 1, 2, 3, 4
Solutions	Section 4.7: 1, 2, 3 Section 4.8: 1, 2, 3, 4, 5, 7 Section 4.9: 1, 2
Solutions	4.10.6
Solutions	Section 4.10: 1�C5 Section 5.1: 1�C7, 9 (labeled 8), 10 (labeled 9), 11 (labeled 10), 12 (labeled 11)
Solutions	Section 5.2: 1, 2, 3 Section 5.3: 1�C7, 9, 11
Solutions	Section 5.3: 8, 10, 12, 13 Section 7.1, 7.2: ��
Solutions	Section 7 �� Section 5.4: 1�C7
Solutions	Section 5.4: 8, 10 Section 5.6: �� (labeled 5.5)
Solutions	Section 5.7: �� (labeled 5.6) Section 6.1: 1, 2, 3, 5, 7, 8, 10, 11
Solutions	Section 6.3 (labeled 6.2): 1, 2, 3 Section 6.6 (labeled 6.3): 1, 3 (labeled 2), 4 (labeled 3), 5 (labeled 4), 6 (labeled 5), 7 (labeled 6) Section 6.4: 1, 2, 3, 4 (labeled 5), 6 (labeled 5),
Solutions	Section 6.7 (labeled 6.5): 1, 2, 4 (labeled 3), 5 (labeled 4), 6 (labeled 5), 8 (labeled 7) Section 6.8 (labeled 6.6): 2, 3, 7 (labeled 4), 8 (labeled 6), 10 (labeled 7)
Solutions	Section 10.1: 5, 7, 10 Section 10.2: 1, 2 Section 10.4: 1, 2, 3, 6
Solutions	Section 10.1: 3, 4, 7, 8, 10 Section 10.2: 1, 2

Publisert 14. jan. 2021 - Sist endret 13. mars 2025