1: topologies

2: local dimension

1: So, yesterday, I guess I was using the box topology to build my infinite dimensional "boxes". Prof Day suggested I use the product topology instead. However, I think open sets in this topology must be the infinite product of sets Vi with only a finite number of these sets not equal to the real line. But then is the complement of my fractal open? Does that mean that my fractal isn't closed? But I know my fractal is compact since I know the infinite product of compact sets is compact. But wouldn't the infinite product of the unit interval should also be compact?

2: As for local dimension, I'm probably gonna scrap the "official" definition and just work with my own definition. I'm gonna try out some Matlab experiments on the HÃ©non attractor. I've gotta try to work out some things with GAIO.

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