2018-12-04

I spent some time reading about the Riemann–Stieltjes integral in Apostol’s Mathematical Analysis. (I wanted to see how some other books defined this.)

I also spent some time thinking about the nested intervals theorem.

I started reading James Munkres’s Topology. I finished reading section 1.1 (set theory and logic) and thought about/did some of the exercises (they are the kind of exercises I am familiar with from other texts, so I don’t plan to work through all of them). One particular exercise caught my eye, which was exercise 1.1.2(k)–(l); this is because I had seen the same exercise in Tao’s book a while back. Since I fell into the trap on my first attempt (when working through Tao’s book), I had wanted to “get back at” the problem by explaining it clearly (I didn’t find any excellent explanations online). This seemed like the right opportunity, so I started the page Conjunction of subset statements versus Cartesian product subset statement.