## Dr. Sarah's Math 4710 Web Page - Fall 2001

• Class Highlights-Day by Day
• Dr. Sarah's Schedule
• WebCT Includes bulletin board and grades
• Proof-Writing Samples
• Proof-Writing Checklist
• WebCT Test Questions
• ### DUE/REVISION Dates

 Date WORK DUE at the beginning of class or lab unless otherwise noted! Dec 8 - Sat Final Project PowerPoint DUE as an attachment to greenwaldsj@cp.appstate.edu by 11:30am. Talks are 12-2pm. Knots and Links part 1, Knots and Links part 2, Knots and Links part 3, by Matt Lawson Euler Characteristic, by Matt Mellon Topology of the Universe, by Dorothy Moorefield Dec 5 - Wed Problem Set 10 Revisions due by 5pm WebCt Test 5 retakes due by 11:55pm Dec 4 - Tues Organizational Plan of Talk In my office or on reserve in the library under Greenwald - Math 1010 - Heart of Mathematics skim thru p. 288-397. WebCT Test 5 on Heart of Math reading, quotient spaces, connected and compact spaces and classification of spaces. Nov 29 - Thur Abstract of Talk WebCT Test 4 retakes due by 11:55pm Nov 27 - Tues Problem Set 8 revisions due by 5:15 pm Nov 20 - Tues Problem Set 10 DUE Tuesday 11/20 at 5pm, Revisions DUE Wed Dec 5th Prove that If X is compact Hausdorff under both T and T', then T=T' or they are not comparable. Show that the union of two compact sets in a space X is compact in X. Show that the intersection of two compact sets in a Hausdorff space X is compact in X. Show that Hausdorff is required in the above statement, ie that the intersection of compact subspaces of a space X is not necessarily compact as follows:       Look at Y=[0,1] U [2,3] with the equivalence relation ~ on Y s.t.    t ~ t for all t,    t ~ t+2 for all t in [0,1),    t ~ t-2 for all t in [2,3)       Show that Y/~ is not Hausdorff       Show that [0,1] U [2,3) is compact in Y/~       Show that [0,1) U[2,3] is compact in Y/~       Show that the intersection of these two compact sets in Y/~ is not compact in Y/~ Nov 16 - Fri Problem Set 9 DUE Friday 11/16 at 5pm No revisions. Using ideas of connected spaces, show that no pair of the following is homeomorphic:   (0,1),   (0,1],   [0,1] Using ideas of connected spaces, show that   R^2 and R   are not homeomorphic Show why each of the following is or is not connected:   R_l,   R_zar=R_fc,   R^2_zar
• Problem Set 8 DUE Friday 11/9, Revisions DUE Mon 11/26 by 6pm See hints (parts 1 and 2) on WebCT bulletin board
Section 2.6 numbers 1, 2, 5, 9, 17b

• WebCT test 4 Thur 11/8 - Retakes DUE Thur 11/29 at 11:55pm on all sections we have covered so far except 2.6

• Preliminary Bibliography for final project DUE Tuesday 11/6

• Problem Set 7 DUE Fri 10/26 See hints on WebCT bulletin board
Section 2.1 numbers 6, 7, 9, and 19 parts c and d, and then prove part b.
Section 2.2 numbers 2 and 4

• Problem Set 6 DUE Wed 10/17 Revisions DUE Wed 10/31 See hints on WebCT bulletin board
Prove that X is discrete iff every function f : X-->R is continuous, p. 57 #20,
Prove or Disprove that the following are homeomorphic
a) S^1 and {(x,y) | max(|x|,|y|) = 1}, both with the subspace topologies of R^2.
b) [1,2) and {0}U(1,2) with the subspace topologies of R^2
c) R with the standard topology and R_cf with the finite complement topology.

• WebCT test 3 on 1.1-1.4 Thur 10/4, Retakes DUE Wed 10/17

• Problem Set 5 DUE Wed 10/3, Revs DUE Tues 10/9
p. 159 number 14, and
Prove that X is Hausdorff iff Delta={(x,x) | x in X} is closed in XxX

• Problem Set 4 DUE Wed 9/26
Section 1.4 4,5, 12, 14, 17, 18 (informal justifications on the last 4)

• WebCT test 2 on 1.1-1.3 Thur 9/20 (but meet in 105 first) RETAKES DUE Tuesday October 2

• Problem Set 3 DUE Wednesday 9/19
p. 24-26 numbers 5, 7, 17, 18, 20 and 21 (informal justifications on all but 5)

• Project Topic DUE Tuesday 9/11

• Problem Set 2 DUE Tuesday 9/4

• WebCT quiz on Thursday 8/23 - study topology ad, syllabus, class notes, and the "orange poster" on my door - 326 Walker. Retakes DUE Sept 12.

• Problem Set 1 DUE Tuesday 8/21