The lectures versus the book

This page will be updated more formally later in the course. For now it contains
a few remarks comparing the textbook versus the class lectures.

Jan. 18 -
We have covered Sections 2.8, 4.1, 9.1 only up to (and
excluding) definition 9.1.4, Section 4.3 except perhaps 4.3.10,
and also definition 4.2.1 and lemma 4.2.2. Furthermore, we covered 4.4.3
and mentioned 4.4.4, and also 9.2.1 and the first part of 9.2.2.

However, there is a difference with regard to Sections 4.2, 4.3,
and part of 4.4: we are doing
this material for general metric spaces, not just for R^n; related to
that, we start with definitions of open and closed sets and closure that are more
general than the book's, and the book's definitions will soon become theorems for
us. Finally, our treatment of closure was more thorough, so that we started
on limit points of sequences, whereas the book only defines limit points of sets.
Similarly, we use definition 9.2.2 for compactness, and the definitions in Section
4.3 will, again, soon be theorems.
During this week and part of next we will be covering the proof of Theorem 4.4.6, but
before that, much of the rest of Section 9.2. Section 9.3 will come after that,
along with some extras.