Friday, June 6, 2008

6/6 (Friday!)

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 Hénon attractor. I've gotta try to work out some things with GAIO.

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