Topology

Hw set 1 for wed
1.3: 1
2.1: 2, 3, 4, 5

3.1: 1, 4 (See chapter 2 for definition of seperable metric space)

Hw set 2 for wed
3.1: 2, 4, 6 (extra credit), 8

Let Y be the topological space from the lecture, which was the quotient of L1 ⊔ L2 by the equivalence relation: (x,y) ∈ L1 is equivalent to (z,h) ∈ L2 iff x = z and x > 0. Here L1, L2 are parallel horizontal lines in R². This space looks like the letter Y. Show that this space is not metrizable with its quotient topology.

Hw set 3 for wed 3.2: 1,2,3,4,6,10

Hw set 4 for wed 3.2: 12
3.3: 1,2,3

Hw set 5 for wed

3:3: 4, 5, 6, 7, 8, 9 (extra credit)

HW set 6

3.3: 10 3.4: 1, 2, 3

HW set 7

3.4: 4, 5, 6,

HW set 8

3.4: 5, 6, 8, 9, 10, 11

Set 9
5.1: 1, 2, 3, 4

Set 10:

5.1: 5,6,7

Set 11:

5.2 1,2

–> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –> –>