Math 202A UCB, Fall 2012 M. Christ
Problem Set 8, Due Wednesday October 24
(8.1) Text problem X.6.
(8.2) Text problem X.11.
(8.3) Text problem X.16.
Let U be a locally nite open cover of a normal topological space X . Show that there exists
a collection o
Math 202A UCB, Fall 2012 M. Christ
Problem Set 7, Due Wednesday October 17
(7.1) Text problem X.3.
This problem establishes a close cousin of Baires theorem for locally compact Hausdor spaces.
(Since a complete metric space need not be locally compact, th
Math 202A UCB, Fall 2012 M. Christ
Problem Set 6, Due Wednesday October 3
The following fact (also frequently used in Math 185), which relates uniform convergence to convergence of integrals, could be helpful in one or more of this weeks problems: Let a b
Math 202A UCB, Fall 2012 M. Christ
Problem Set 5, Due Wednesday September 26
This weeks problem set is intended to be more straightforward. (5.2) is an application which
involves concepts which we havent been working with directly, but an outline is inclu
Math 202A UCB, Fall 2012 M. Christ
Problem Set 4, Due Wednesday September 19
This weeks problems are concerned mainly with compactness and the Baire category theorem. Be
sure to read sections 1-7 and 9 of Chapter II of our text.
(4.1) Let E, F be nonempty
Math 202A UCB, Fall 2012 M. Christ
Problem Set 3, Due Wednesday September 12
(3.1[a]) Show that any Cauchy sequence which has at least one convergent subsequence, is itself
convergent.
(3.1[b]) Show that any Cauchy sequence is bounded.
(3.2) Let (X, d) be
Math 202A UCB, Fall 2012 M. Christ
Problem Set 2, Due Wednesday September 5
This weeks problem set includes more problems, but most are shorter/easier.
The convention in this course is that unless the contrary is explicitly indicated or unless it is
clear
Math 202A UCB, Fall 2012 M. Christ
Problem Set 1 (Due Wednesday 8/29)
Notation. R, Z, Q = sets of real numbers, integers, and rational numbers, respectively. N =
set of all natural numbers = cfw_1, 2, 3, 4, . Ao = interior of a set. Acl = closure of a set
Mathematics 202A, Fall 2012 M. Christ
Midterm Exam Solutions and Comments
Distribution of scores: Total points: 45. High score: 43. 90th percentile 38. 80th:
33. 70th: 28. 60th: 25. 50th: 23. 40th: 21. 30th: 20. 20th: 18. 10th: 16.
(1a) Let (X, d) be a me
Mathematics 202A, Fall 2012 M. Christ
Midterm Exam Solutions and Comments
Distribution of scores: Total points: 45. High score: 43. 90th percentile 38. 80th:
33. 70th: 28. 60th: 25. 50th: 23. 40th: 21. 30th: 20. 20th: 18. 10th: 16.
(1a) Let (X, d) be a me