MAT 441C
HW #7
4/9/13 (due Friday 4/12/13 at 5:30 pm)
25 points
Name
Justify all answers. Unsupported answers may not receive full credit.
1. Let M be the 1-sphere S 1 = cfw_(x, y) R2 | x2 + y 2 = 1.
MAT 441C HW #4 Name w
2/27/13 (due Wednesday 3/6)
25 Juaty I m. 0mm when my an: nun- (III audit.
1. (a)SupposeXisatopologicalspaoe.nndAisaconnectedsubspaceofX. SuppoeeAngz.
ProveBisconnected.
Supp
w
as. . t a b
MAT 441C I-IW #5 Name E {mote
3/7/13 (due Monday 3/11 at 5:30 p111)
25 pomts Justify all answars. Unsupported answers Inny not, receive fun credit
E. Let X r {1,1} >< [«1,1]. (So X i
MAT 441C
4/1/13 (due Friday 4/5/13)
25 points
HW #6
Name
Justify all answers. Unsupported answers may not receive full credit.
1. Let X and Y be topological spaces, and suppose Y is compact.
(a) Let x
MAT 441C HW #6 Name
4/1/13 {due Friday 4/5/13)
25 pomi-S Justify n11 z-mswnrg. Unsunperted answers may nor receive fuil credit
1. Let X and Y be topological spaces, and suppese Y is compact.
Let :
MAT 441C
2/27/13 (due Wednesday 3/6)
25 points
1.
HW #4
Name
Justify all answers. Unsupported answers may not receive full credit.
(a) Suppose X is a topological space, and A is a connected subspace o
MAT 441C
HW #5
3/7/13 (due Monday 3/11 at 5:30 pm)
25 points
Name
Justify all answers. Unsupported answers may not receive full credit.
1. Let X = cfw_1, 1 [1, 1]. (So X is a union of two disjoint lin
MAT 441C
2/9/13 (due Wednesday 2/13)
25 points
HW #3
Name
Justify all answers. Unsupported answers may not receive full credit.
1. Let f : X Y be a continuous function. Let (f ) X Y be the graph of f
MAT 441C
3/15/2013
140 points
Exam 2
Name
1.(30) (a) Suppose X is an innite set, endowed with the discrete topology. Prove that X is not
compact.
(b) Let Y be the set of integers, with the conite topo
MAT 441C
4/19/2013, due Wednesday 4/24
160 points
Exam 3 (Take-home)
Name
Take-home exam rules: you may use texts and notes from lecture, but are not to discuss the exam with any human, by any means (
MAT 441C
1/28/13 (due Monday 2/4)
25 points
HW #2
Name
Justify all answers. Unsupported answers may not receive full credit.
1. A topological space is is called a T1 space if cfw_x is a closed set for
MAT 441C
1/18/13 (due Friday 1/25/13)
25 points
HW #1
Name
Justify all answers. Unsupported answers may not receive full credit.
1. Let X Rn . Show that the open -ball BX (x, ) is an open subset of X,