Math 651: Topology --- Spring 2021

To contact the instructor: j.rhodes@alaska.edu                  Course Syllabus

Textbook:

Topology, 2nd ed., by James Munkres, Prentice Hall

LaTeX resources:

Math into LaTeX (The book for learning LaTeX)

Detexify (A website which lets you draw a symbol and gives the LaTeX code for it)

LaTeX template file for homework

Homework Assignments:

Homework is normally assigned M,W,F; discussed in the lab section the following M; and due by classtime W. Ideally you will complete the homework before the lab discussion, and then use the extra two days to improve it.

• 1/11: p.83 #1, 2 (in your solution refer to the 9 topologies as $\mathcal{T}_1$ - $\mathcal{T}_9$ ordered left->right and then top->bottom), 3, 4
• 1/13: p.83 #7, 8
• 1/15: p.91 #4, 5, 8, 9
• 1/18: NO CLASS
• 1/20: p.100 #3, 5("determine" means "determine and prove"), 8 ("determine" means "prove or disprove"), 13, 16 (since these are examples, you do not need to state formal Propositions, but should still give complete arguments)
• 1/22: p.100 #15, 17, 18
• 1/25: p.111 #4, 8, 11, 12 (you may use Theorem 21.5 on p.131), 13
• 1/27: p. 118 #6, 7, p. 126 #2, 3
• 1/29: p. 126 #4, 6, Q: Explain, as clearly as you can, why trying to metrize \mathbb R^c by following the ideas that work for \mathbb R^\omega fails.
• 2/1: p. 133 #3 (note you must show these are metrics AND they induce the product topology), 4 (the ordered square does NOT have the subspace topology from the ordered plane)
• 2/3: p. 144 #2, 3, 4
• 2/5: Q: pdf
• 2/8: p. 146 #4, 7ab
• 2/10: p. 152 #7, 9, 10; p. 157 #1ac, 2 (use the IVT), 7
• 2/12: p. 157 #8, p.162 #1, 9
• 2/15: p. 170 # 1, 5, 7
• 2/17: p. 170 #8; p. 177 # 1, 3
• 2/19: p. 186 #1, 3, 8
• 2/22: p. 194 #3, 4, 5, 12 -- due MONDAY 3/1
• 2/24: none
• 2/26: none
• 3/1: Midterm In-class, Take-home out
• 3/3: none
• 3/5: none, Take-home due
• Spring Break
• 3/15: p. 330 #1, 3; p.334 #1
• 3/17: p. 334 #3, 6, 7
• 3/19: p. 334 #4; p. 341 #2, 3
• 3/22: p. 347 #3, 5, 8
• 3/24: p. 353 #1, 2, 4abcd
• 3/26: p. 366 #1, 2 (informal explanations that could be developed into proofs are sufficient), 6
• 3/29: p. 366 #3, 7, 9
• 3/31: p. 375 #3, 5, p.421 #2
• 4/2: none
• 4/5: p. 438 #2, 4, 5
• 4/7: p. 483 #1, 2, 4
• 4/9: none
• 4/12-16: See pdf
• 4/19: Takehome exam out, due 12:00 noon 4/28
• 4/29: Inclass exam, 1:30pm