First section here was on homeomorphisms, which is essentially a brief intro in the foundations of topology. I've been wanting to study topology for years, but as is the trend, I didn't have time to dwell. Again, we don't get examined on topology, so this will be something I'd want to come back to after my final exam.

Next up was "closed and open sets revisited", which is practically exactly what you expect.

The third section introduced the concept to connectedness properly, and the fourth went on to explore connectedness in Euclidean space.

At this point, I'd learned enough to tackle the assignment questions. I didn't read through the last two chapters, "path-connected spaces" and "the topologists cosine", but I didn't feel too guilty about this. I'm already vaguely familiar with path-connected spaces, and the last section seemed to be unlikely to be examined. I'll review both of these sections during my revision period though.

All in all, this chapter was mercifully easy to understand.