Introduction to Topology
MATH-4040
Fall 2010

 Instructor: Mark H. Holmes Office: Amos Eaton 322 Office Hours: MTr 3-4:30 Phone: 276-6891 Email: holmes

Couse Information and Assignments

Text web-site (contains a "Corrections and Clarifications" section)

HW1 Solutions

HW2: 1.11, 1.12, 1.15, 1.20, 1.21 (due Sept 16) Solutions
note: replace R with R+ in 1.11(d)

HW3: 1.34, 1.36, 2.1(a),(b),(c),(g), 2.4, 2.6, 2.11 (due Sept 23) Solutions
Extra Credit: give an example of an uncountable closed subset of irrationals from the interval [0,1] (note that you need to explain why the set is closed and uncountable)
From the errata page for the textbook:
Page 43, Exercise 1.34. This exercise is incorrect as stated because the discrete topology on the five-point set is the only Hausdorff topology on the set. A suitable replacement would be:
1.34. Prove that on a finite set, the discrete topology is the only topology that is Hausdorff.

HW4: 2.13(e),(f), 2.18, 2.23, 2.24(e),(f), 2.28 (due Sept 30) Solutions

HW5: 3.15, 3.19, 3.20, 3.22 (due Oct 7) Solutions

Exam 1: Oct 14 (covers chapters 1-3) Solutions

HW6: 4.2, 4.23, 4.24, 4.32, 4.26, 5.2, 5.5, 5.9 (due Oct 25) Solutions

HW7: 5.23, 6.1, 6.8, 6.18(a),(c),(d), 6.41, 6.44(n=2), 6.46 (due Nov 4) Solutions

HW8: 7.1, 7.3, 7.8, 7.11, 7.15, 7.24, 7.35 (due Nov 11) Solutions

Exam 2: Dec 6 (covers chapters 3.3-7, 14.1)