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pdt @lemmy.sdf.org

free the electrons! • elementary particles of the world, unite!

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What's an example of an ordered set other than R that obeys the first 3 Suslin conditions?
  • 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.

  • What's an example of an ordered set other than R that obeys the first 3 Suslin conditions?
  • I didn't mean IR^n with its usual topology. I meant IR^n with the order topology for the dictionary order. IIANM you can construct an uncountable set of pairwise disjoint open intervals in this topology so it can't have a countable dense subset. But as I said it's been years since I touched a topology book.