I’ve been working through Michael Barnsley’s book, “Fractals Everywhere”; it’s a relatively advanced textbook on fractal geometry. The first chapter is a survey of analysis and topology, which has been a nice opportunity to refresh my math skills, as well as a more thorough exploration of metric spaces than I’d gotten before. I was double checking one of the problems and wrote it out all organized, and then I decided to tell you about it. So I scanned it in, started cleaning it up in GIMP, one thing led to another…

Learnin me some GIMP skillz

I later realized that I could actually generalize the bulk of the proof into a lemma: Any subset of a totally bounded set is itself totally bounded.

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