1: So, today I took a break from Matlab and most of the day, I worked on entering my definitions and proofs that I have so far into Tex. Using Tex isn't as hard as I thought it would be. It's not so bad once you get used to it. I still am hoping they have some kind of Tex workshop to show us how to do the Powerpoint with Tex.
2: I reviewed definitions of topologies and bases and fractals and products, trying to get an idea of how to define an infinite dimensional fractal and infinite dimensional fractal dimension. Nothing came straight to mind, but I have some ideas of what I can look at. I'm still not sure how changing the topology of a space affects box-counting dimension. I tried looking at the box-counting dimension of the Cantor set in R with the discrete topology to help, but I don't see how changing the topology really gives you a different answer. I guess it's supposed to change your definition of a box? I can see how maybe a different metric might change things, but the topology?
I'll probably end up back on Matlab tomorrow, organizing all my graphs and doing some other things. Prof Day also suggested I try to prove something about local dimension and scaling for uniform fractals like the Cantor Set. I also need to visit IT tomorrow since I didn't today.