Homework Assignments

• Assignment #1 (due Sept. 4):
  Rudin p.21: #1, 2, 5, 8, 13, 14, 15, 17, 18
  Building Proofs: 1.4 #3ad, 1.8 #2, 1.10 #1, 1.15 #1cg & #2d

• Assignment #2 (due Sept. 11):
  Rudin p.43: #2-6, 8, 9, 10 (skip last question), 11

• Assignment #3 (due Sept. 18):
  Rudin p.43: #10 (Which are compact?), 12, 14, 15, 16, 22
  A. Prove that the closure of S is equal to the union of S and the boundary of S.
  B. Prove that the boundary of S is closed.

• Assignment #4 (due Sept. 25):
  Rudin p.43: #19, 20, 23, 25 (Rephrase: Prove that every compact metric space K is separable and has a countable base.), 26
  p.78: #1, 2 (use A below)
  

• Assignment #5 (due Oct. 4):
  Rudin p.78: #3, 4, 5, 16, 20
  

• Assignment #6 (due Oct. 16):
  Rudin p.78: #6-10, 12

• Assignment #7 (due Oct. 25):
  Rudin p.78: #13, 21, 22
  p. 98 #1-4
  

• Assignment #8 (due Nov. 1):
  Rudin p.98: #6-8, 11, 14, 15, 19, 20

• Assignment #9 (due Nov. 8):
  Rudin p.98: #16, 21, 22
  p. 114 #1, 2, 5, 7, 12

• Assignment #10 (due Nov. 22):
  Rudin p.114: #11, 14, 22, 25
  p. 138 #1, 2, 3, 4

• Assignment #11 (due Dec. 9):
  Rudin p.114: #26, 27
  p. 138 #5, 7, 10abc, 11, 15, 16

Reading Assignments

• Rudin: p. 1-17, 17-21 ("for interest"), 24-43, 47-78, 83-98, 103-113, 120-137

• Building Proofs: all sections except 1.14

Exams

• Final exam: Thursday Dec. 19, 9:45-11:45 am

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