Read Chapters 1 and 2 of H.L. Royden, Real Analysis, Third Edition, 1988.
You are responsible for all questions below. Please hand in
complete
solutions to the starred problems only. The page numbers refer
to
H.L.
Royden, Real Analysis, Third Edition, 1988. You should give complete
and rigorous arguments in answering each question. This
homework
should be turned in no later than Monday, February 4, 2008.
Page 8: 4, 5*.
Page 12: 6*, 7.
Page 16: 9, 11, 12, 13, 14*, 16*, 17, 18*.
Page 19: 19, 20*.
Pages 22-23: 23, 24*, 25.
Page 26: 30*.
Page 27: 31, 33.