* denotes a suggested problem. You should know how to complete a * problem, but it will not be graded (so please do not hand it in).

Due Wednesday, September 18

A. Consider \(\mathbb{R} \times \mathbb{R}\) with the lexicographical (dictionary) order topology. (a) What topology does \(\mathbb{R}\times 0\) inherit as a subspace? (b) What topology does \(0\times \mathbb{R}\) inherit as a subspace?

Section 16 problem 6

Section 17 problems 3, 4, 6, 8*, 9, 11*, 15*