Again, this chapter was fairly merciful. First section was a natural progression from the last chapter, namely continuity of functions from to and a return to the all important triangle inequality from my complex analysis module last year.

Next section was great as it introduced a new mathematical object: the metric. Always fun, learning about something new like this. Though something that really tripped me up (that I feel I'm still struggling with now) is the geometry of metric spaces. There are sets defined around points in spaces called "balls", be it open or closed. I seem to have a big problem with defining what are inside and outside of these circular (in 2D) sets based on their defined radii. Sounds simple, but it seems it's not very intuitive. Not being able to define what's in your set is bad, so I need to do some further reading on this.

Next up was sequences in metric spaces, followed by the definition of continuity in metric spaces.