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 R^{n}. Show that there are countably many open balls
B_{1}, B_{2}, B_{3}, ... such that
V= B_{1} U B_{2}
U B_{3} U ...
A subset E of Euclidean Space is sequentially compact if every sequence
x_{k} in E has a convergent subsequence x_{kj} whose
limit belongs to E. Prove that every compact set is sequentially compact.