this post was submitted on 07 Aug 2023
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[โ€“] [email protected] 2 points 1 year ago (1 children)

I think you could just take an open interval in the order topology and then create a collection by turning the first dimension into a parameter. IIANM for each value of the parameter you'd get an open set, they'd be pairwise disjoint, and there'd be uncountably many of them.

[โ€“] [email protected] 2 points 1 year ago

Ah, you're right, why didn't I think of that? Thanks for all the help!