• CanadaPlus@lemmy.sdf.orgOP
    link
    fedilink
    arrow-up
    1
    arrow-down
    1
    ·
    1 year ago

    IIANM you can construct an uncountable set of pairwise disjoint open intervals in this topology

    Hmm. Do you have a construction in mind?

    • pdt@lemmy.sdf.org
      link
      fedilink
      arrow-up
      2
      ·
      1 year ago

      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.