MATH 554  Math 703 I
Analysis I
Homework Assignments and Supplementary Materials
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Homework Assignments
(Each Problem is worth 10 pts.)
No.  Assignment Due  Page and No.'s  Solutions 
#1 
Wednesday (1/21) 
In problems 12, assume F is a field:


#2 
Friday (1/30) 
Additional Graduate Student Problems: Page 30: 11 

#3 
Friday (2/06) 


#4 
Friday (2/13) 
Click here to download the assignment.  
#5  Monday (2/23)  Click here to download the assignment.
Extra Credit (15 pts.) Prove the following about closure of sets:

Main E.C. 
#6  Friday (2/27)  Problem:
Suppose that S has the property that each sequence from S which
converges, must converge to a limit which belongs to S. Prove that
S is a closed set.
Extra Credit (10 pts.) Complete the proof of the following: Suppose in the real numbers the sequence {b_{n} } converges to b and b is not zero. Prove that 1/b_{n} converges to 1/b. 

#7  Friday (3/26)  You can download homework assignment #7 for Friday March 26, here.  
#8  Friday (4/9)  Problem:
Using properties of connectedness and the last theorem
proved in Monday's lecture (about continuity of inverse functions),
prove that for each natural number n:
Extra Credit (10 pts.) Fill in the details of the proof begun during Monday's lecture: Prove that a function is continuous if and only if the inverse image of a closed set is closed. Be sure to prove the set equality relating inverse images of the complements of sets. 





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