M351 Real Analysis
Dr. Leary
Cianna Duringer
Polished Problem #4.4.4 Revision 1
Q: Give an example of a sequence of open sets G1, G2, G3, whose intersection is
neither open nor closed. Why does this not contradict Theorem 4.17?
A:
Let Sn = (0, 1+1/n), n=1

M351 Real Analysis
Dr. Leary
Cianna Duringer
Polished Problem #3, Original
4.3.4
November 15th, 2015
Question:
A careless student, when asked, incorrectly remembers that a set is open if it
contains all of its interior points. Is there an example of a set

M351 Real Analysis
Dr. F Leary
Cianna Duringer
Problem 4.2.3, Polished Problem #2
Revision #2
11/12/2015
Q: Show that every interior point of a set must also be an accumulation point of that
set, but not conversely.
A:
Let E be a set of real numbers. Let

M351 Real Analysis
Polished Problem
Problems 3.4.3 and 3.4.4
Revision edition #5
Cianna Duringer
Note: For each summation, the index begins at k=1 and continues to .
Question: If (ak + bk) converges, what can we say about the series
ak and bk?
If (ak + b