October 10th, 2000

beartato phd

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Went to OS review session.
New topo homework is sort of annoying.

Thoughts on stratifiability:
recovering a stratification from just the open sets
is relatively easy (and it does seem to need T1 so that each
stratum has no accumulation points) but hard to recover
it from just the points.
Straightforward proof of open stratifiability = metrizability
(modulo isolated points) fails because the 'escape velocity'
condition isn't quite strong enough to guarantee *uniform*
shrinkage of strata elements.
T0 + no isolated points => open sets are infinite?

Cohen forcing is beginning to make a lot more sense
than it once did to me. The topos-theoretic approach
is still nowhere near comprehension, though.