i hope that we get a chance to talk this wednesday morning...
i have a question about boolean toposes and related stuff that's really bugging me...
(seems like things like this have been bugging me for a long time... i think there's hope i'll get it straightened out eventually though...)
did i mention that this is probably a very stupid question??? ....
the category of boolean algebras is allegedly equivalent to the opposite of the category of totally disconnected compact hausdorff (tdch for short) spaces... i think that i understand reasonably well how this works...
consider the one-point compactification of the discrete space "N" of natural numbers; this is tdch. the corresponding boolean algebra consists of the clopen subspaces, which in the tdch case is equivalent to the regularly open subspaces, i think. we can also think of them as the subsets of N which are either finite or co-finite, or the sequences of truth-values that are eventually constant.
now in the topos of sheaves over this tdch space, ... ???....
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