| Date |
WORK DUE at the beginning of class or lab
unless otherwise noted! |
| Dec 8 - Sat |
|
| 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
|