Math 142, Spring 2013. HW8 Solutions
4. Consider a homomorphism f : 1 (S1 , 1) 1 (S 1 , 1); this morphism is completely determined by the value f (1) (since, for n > 0, f (n) = f (1 + 1 + . + 1) = f (
Math 142, Spring 2013. HW3 Solutions
3. a) Write
S = Q1 Q2 Q3 Q4 ,
where Q1 is the east quadrant in S, Q2 is the north quadrant in S, Q3 is the west quadrant
in S, Q4 is the south quadrant in S. For e
Math 142, Spring 2013. HW2 Solutions
3. a) Let A X , with X a topological space. Then, A is the intersection of every closed set
that contains A,
A=
F
AF
F closed in X
Thus, as this is an arbitrary in
Math 142, Spring 2013. HW7 Solutions
2. a) Denote the constant map with with domain I , R and image cfw_0 I , R, by f0 , by abuse
of notation; hence, f (x) = 0, for each x I , R. Dene the homotopies
H
Math 142, Spring 2013. HW5 Solutions
1. Let A X be connected.
a) If A is closed then A = A so the statement is trivial. Assume that A = A and suppose
that A is not connected. Then, there are nonempty
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#1
Curtis Tekell
Prof. Kate Poirier
February 11, 2013
Exercise 1. Consider with its standard metric 0 , (, ) =
.
(a) Prove that the standard metric on is indeed a metric.
(b) Consider with i