# Classnotes for November 15

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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

## LaTeX notes

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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 $\mathbf{X}=\mathbb{Z}$ and define $\mathbf{B}_n=\{2n-1,2n\}$ for each n. Obviously the collection of all $\mathbf{B}_n$ is a basis for a topology on $\mathbf{X}$. Notice that with this topology $\mathbf{X}$ is not compact: the same family of all $\mathbf{B}_n$ is an open cover of $\mathbf{X}$ with no finite subcover. But $\mathbf{X}$ is limit-point compact: suppose that $\mathbf{A}$ is an infinite subset of $\mathbf{X}$ and $a\in \mathbf{A}$. 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 $\mathbf{A}$.