INSTRUCTOR:   Charles Conley,  GAB 475,  (940) 565-3326

OFFICE HOURS:   Tuesday and Thursday 1:00-3:00, and by appointment

CLASS MEETS:   TR 11:00-12:20, GAB 204

EXAMS, HOMEWORK, AND GRADING: There will be two 100 point midterms, on Tuesday, Feb. 19 and Tuesday, April 2, and a comprehensive 180 point final on Tuesday, May 7, 10:30-12:30.  There will also be twelve 10 point homeworks, due Thursdays at the beginning of class.  There will be no make-up exams except for emergencies, and late homework will be worth half-credit.

TEXT AND PREREQUISITES: The text is Topology, second edition, by James Munkres.  The prerequisite is Real Analysis (Math 2510-20).

TOPICS:   We will cover most of the first four chapters of Munkres' book, and as time permits, parts of the fifth, seventh, and eighth.  We will begin with some of the set theory and logic underlying topology, followed by the definition of abstract topological spaces.  The concepts of continuous functions, compactness, and connectedness will be central, and rigorous proofs will be emphasized.  Most of our examples will be metric spaces, but we will also look at some of the standard counter-examples associated to the separability axioms.  We will conclude with some discussion of function spaces, one of the motivations for the original theory.  The contents of  Part~I of the book are given below.  Unfortunately we will not have time to go into Part~II, which concerns algebraic topology and homotopy theory.

Chapter 1:  Set Theory and Logic

Chapter 2:  Topological Spaces and Continuous Functions

Chapter 3:  Connectedness and Compactness

Chapter 4:  Countability and Separation Axioms

Chapter 5:  The Tychonoff Theorem

Chapter 6:  Metrization Theorems and Paracompactness

Chapter 7:  Complete Metric Spaces and Function Spaces

Chapter 8:  Baire Spaces and Dimension Theory
 

FINAL EXAM:   Tuesday, May 7, 10:30-12:30
 

HOMEWORK  12,  Due Thursday, May 2:

   Section 26:  7
   Section 27:  2de
   Section 28:  2, 3b, 7a
 

HOMEWORK  11,  Due Thursday, April 25:

   Section 26:  4, 5, 6
   Section 27:  2abc, 4
 

HOMEWORK  10,  Due Thursday, April 18:

   Section 23:  1
   Section 24:  1, 2, 3, and the first sentence of 11 for R^2
   Section 25:  The second sentence of 1
   Section 26:  1a, 2a, 3
 

HOMEWORK  9,  Due Thursday, April 11:

   Section 21:  6, 8 for X = Y = R
   Section 23:  2, 4 for R_Z, 5, 7, 9, 12
 

EXAM 2:   Tuesday, April 2
 

HOMEWORK  8,  Due Tuesday, April 2:

   Section 18:  11 for F: R^2 --> R and 13 for X = R^2, Y = R
   Section 21:  1, 2, and 3a for n = 2
   There are also 3 extra problems I handed out on a worksheet.
 

HOMEWORK  7,  Due Thursday, Mar. 14:

   Section 18:  4 for X=Y=R, 5, 7a, 8 for R, 10 for A=B=C=D=R, 11 for X=Y=Z=R
   Section 20:  1a for R^2, 2, 3a
 

HOMEWORK  6,  Due Thursday, Mar. 7:

   Section 17:  10 for R, 11 for R x R, 12 for R, 16b for R, R_l, and R_Z
   Section 18:  1, 2 for f from R^2 to R^2, 6
   Note: 5 and 7a in Section 18 are postponed to Homework 7.
 

HOMEWORK  5,  Due Thursday, Feb. 28:

   Section 17:  2, 3, 4, 6, 9: do these with X and Y equal to R, the real line.  Also do 16a for R, R_L, and R_Z, 17 for R_L, and 18CD.
   Note: problems 10, 11, 12, and 16b are postponed until Homework 6.
 

EXAM 1:   Tuesday, Feb. 19.  The review sheet will be given out on Feb. 12 and Feb. 14 will be a review day.
 

HOMEWORK  4,  Due Thursday, Feb. 14 (due date changed to Feb. 19, the day of the test):

   Section 13:  4c, 7 (but skip the second topology), 8
   Section 14:  1, 3, 4, 6, 7, 9
 

HOMEWORK  3,  Due Thursday, Feb. 7:

   Section 10:  1, 2, 3, 5, 6
   Section 13:  1, 3
 

HOMEWORK  2,  Due Thursday, Jan. 31:

   Section 6:  1b, 2, 3, 7
   Section 7:  1, 3, 5aefij
   Section 9:  1, 2b, 3, 8
 

HOMEWORK  1,  Due Thursday, Jan. 24:

   Section 1:  1, 2e, 3a, 4d, 7F, 8, 10c
   Section 2:  1, 2, 4abcd, 5ab, 6
   Section 3:  1, 2, 4, 9, 11, 12, 13
   Section 4:  2k, 8b
   Section 5:  1, 4ad, 5cd