MCS 332 Assignments

Date Section Problems Remarks Due
2/11 1-7 Scan these sections. F 2/15
2/13 1 2 Omit explanations. M 2/18
2/15 3
7
15
5
Dictionary order
Omit explanations.
M 2/25
2/18 8 7 Extra credit M 2/25
2/18 9 Entertainment: Problem 6
2/18 10 1, 3 Well-ordering problems M 2/25
2/20 20 9, 10 Euclidean & "l2" metrics M 2/25
2/22 20 lim ||x||p = square norm
Three problems
Extra credit
Required problems
M 3/4
2/25   Prove the Borel-Lebesgue theorem. JM, KP, ET & EP W 2/27
3/1 12, 13 2, 4 Topologies & bases M 3/11
3/4 14
15
16
4, 6, 10 Order topology
Product topology
Subspace topology
M 3/11
3/6 17 6, 7, 8 Closed sets and limit points M 3/11
3/8 17
18
12
1
Hausdorff spaces
Continuous functions
W 3/13
3/18 20
20
21
3: continuity of distance
8: topologies on omega-tuples
7: uniform continuity topology
3: AG & KP
8: JM, EP, ET
7: volunteer
F 3/22
3/18
3/22
20
21
3, 8
7
Hints
Exercise 20.3 (ps)
Exercise 20.8 (ps)
W 3/27
3/25 23 (2 or 5) and 10 Connectedness F 4/12
3/27 24 3
5
Cf. MCS 331 Exam 2b
Cf. old HW, Exam 1b
F 4/12
3/27 24      
4/8 25
26
1
4
S&S p. 32
 
F 4/12
M 4/15
4/10 26      
4/12 26, 28
+S&S
  27.6: Cantor set
(recommended)
 
4/15 27 Student presentations Use transparencies.  M 4/15
4/17 28, 29 Look at #29.6 .
4/19 20-29 In-class exam
Take-home problems
Closed book
Open book
F 4/19
M 4/22
4/22 30 1, 5   M 4/29
4/24 31 handouts spreadsheets M 4/29
4/26 30-31   Presentations Grid: Space by Hereditary? Products?  
4/29 32 1 Normality is weakly hereditary. M 5/6
5/1 33 3
1
Urysohn's lemma is easy in metric space.
33.1: Extra credit
M 5/6
5/3 34,35,40,11 35.1 Whirlwind tour: See Thms 34.1, 35.1, 40.3, Ex. 11.8. M 5/13
5/6 37 1
A Tychonoff problem (ps) (pdf) (html)
Draw epsilon-ball centered at 0 in D-metric if epsilon=1/4 for Fri. M 5/13
5/8 43 5
9
#43.5 Hint 4 
#43.9 Hint (a) 
W 5/15
5/10 43-44   AG presentation  
5/13 43 #43.5, #43.9 Student presentations  
5/15 45   Extra credit: #45.3 W 5/22
5/17 Sprecher 35-37