Classnotes for November 15
From 0506Topology
| # | Week of... | Links (edit) |
|---|---|---|
| Fall | ||
| 1 | Sep 12 | About, Tue, Thu, Std2Disc |
| 2 | Sep 19 | Tue, Thu, HW1, 14 Sets |
| 3 | Sep 26 | Tue, Thu, Photo |
| 4 | Oct 3 | Tue, Thu |
| 5 | Oct 10 | HW2, Tue, Thu |
| 6 | Oct 17 | Tue, Thu, HW3 |
| 7 | Oct 24 | Mon, Tue, Thu |
| 8 | Oct 31 | Tue, Thu, HW4 |
| 9 | Nov 7 | TE1, Tue, Thu |
| 10 | Nov 14 | Tue, Thu, HW5 |
| 11 | Nov 21 | Tue, Thu |
| 12 | Nov 28 | Tue, Thu, HW6 |
| 13 | Dec 5 | Tue, Thu |
| E | Dec 12 | TE2 |
| Spring | ||
| 14 | Jan 9 | Tue, IT83, Thu, HW7 |
| 15 | Jan 16 | Tue, Thu |
| 16 | Jan 23 | Tue, HW8, Thu |
| 17 | Jan 30 | Tue, Thu |
| 18 | Feb 6 | TE3, Tue, Thu |
| 19 | Feb 13 | Tue, Thu |
| R | Feb 20 | |
| 20 | Feb 27 | Tue, Thu, HW9 |
| 21 | Mar 6 | Tue, Thu, HW10 |
| 22 | Mar 13 | Tue, Thu |
| 23 | Mar 20 | Tue, Thu, HW11 |
| 24 | Mar 27 | Tue, Thu |
| 25 | Apr 3 | Tue, Thu, HW12 |
| 26 | Apr 10 | Tue, Thu |
| Study | Apr 17 | Office Hours |
| Exams | Apr 24 | Final, PM |
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Available [1] (http://katlas.math.toronto.edu/0506-Topology/images/0/02/05-11-15.pdf)
An example of a limit-point compact topological space that it is not compact: Let 
and define 
for each n. Obviously the collection of all 
is a basis for a topology on 
. Notice that with this topology is not compact: the same family of all is an open
cover of with no finite subcover. But is limit-point compact: suppose that 
is an infinite subset of and 
. Define x = 2n − 1 if a is even, and x = 2n if a is odd. Then every open set that contains x also contains a, so x is an accumulation point of .
