Please study the following exercises from the text "Introduction to
Analysis, Second Edition" by William Wade, Prentice Hall 1999.
264[ 1, 6].
Write up
264[ 1c, 2, 5, 7a ].
Here are the equivalent exercises for those using the First Edition:
239[ 4c, 5 ],
Let V be an open set of Rn. Show that there are countably many open balls
B1, B2, B3, ... such that
V= B1 U B2
U B3 U ...
A subset E of Euclidean Space is sequentially compact if every sequence
xk in E has a convergent subsequence xkj whose
limit belongs to E. Prove that every compact set is sequentially compact.